Abramowitz, M. and Stegun, I. (1970). Handbook of Mathematical Functions, Dover, New York.
Agahanov, C. A. (1965). A method of constructing orthogonal polynomials of two variables for a certain class of weight functions (in Russian), Vestnik Leningrad Univ. 20, no. 19, 5–10.
Akhiezer, N. I. (1965). The Classical Moment Problem and Some Related Questions in Analysis, Hafner, New York.
Aktaş, R. and Xu, Y. (2013) Sobolev orthogonal polynomials on a simplex, Int. Math. Res. Not., 13, 3087–3131.
de Álvarez, M., Fernández, L., Pérez, T. E. and Piñar, M. A. (2009). A matrix Rodrigues formula for classical orthogonal polynomials in two variables, J. Approx. Theory 157, 32–52.
Andrews, G. E., Askey, R. and Roy, R. (1999). Special Functions, Encyclopedia of Mathematics and its Applications 71, Cambridge University Press, Cambridge.
Aomoto, K. (1987). Jacobi polynomials associated with Selberg integrals, SIAM J. Math. Anal. 18, no. 2, 545–549.
Appell, P. and de Fériet, J. K. (1926). Fonctions hypergéométriques et hypersphériques, polynomes d'Hermite, Gauthier-Villars, Paris.
Area, I., Godoy, E., Ronveaux, A. and Zarzo, A. (2012). Bivariate second-order linear partial differential equations and orthogonal polynomial solutions. J. Math. Anal. Appl. 387, 1188–1208.
Askey, R. (1975). Orthogonal Polynomials and Special Functions, Regional Conference Series in Applied Mathemathics 21, SIAM, Philadelphia.
Askey, R. (1980). Some basic hypergeometric extensions of integrals of Selberg and Andrews, SIAM J. Math. Anal. 11, 938–951.
Atkinson, K. and Han, W. (2012). Spherical Harmonics and Approximations on the Unit Sphere: An Introduction, Lecture Notes in Mathematics 2044, Springer, Heidelberg.
Atkinson, K. and Hansen, O. (2005). Solving the nonlinear Poisson equation on the unit disk, J. Integral Eq. Appl. 17, 223–241.
Axler, S., Bourdon, P. and Ramey, W. (1992). Harmonic Function Theory, Springer, New York.
Bacry, H. (1984). Generalized Chebyshev polynomials and characters of GL(N, C) and SL(N, C), in Group Theoretical Methods in Physics, pp. 483–485, Lecture Notes in Physics, 201, Springer-Verlag, Berlin.
Badkov, V. (1974). Convergence in the mean and almost everywhere of Fourier series in polynomials orthogonal on an interval, Math. USSR-Sb. 24, 223–256.
Bailey, W. N. (1935). Generalized Hypergeometric Series, Cambridge University Press, Cambridge.
Baker, T. H., Dunkl, C. F. and Forrester, P. J. (2000). Polynomial eigenfunctions of the Calogero–Sutherland–Moser models with exchange terms, in Calogero–Sutherland–Moser Models, pp. 37–51, CRM Series in Mathematical Physics, Springer, New York.
Baker, T. H. and Forrester, P. J. (1997a). The Calogero–Sutherland model and generalized classical polynomials, Comm. Math. Phys. 188, 175–216.
Baker, T. H. and Forrester, P. J. (1997b). The Calogero–Sutherland model and polynomials with prescribed symmetry, Nuclear Phys. B 492, 682–716.
Baker, T. H. and Forrester, P. J. (1998). Nonsymmetric Jack polynomials and integral kernels, Duke Math. J. 95, 1–50.
Barrio, R., Peña, J. M. and Sauer, T. (2010). Three term recurrence for the evaluation of multivariate orthogonal polynomials, J. Approx. Theory 162, 407–420.
Beerends, R. J. (1991). Chebyshev polynomials in several variables and the radial part of the Laplace–Beltrami operator, Trans. Amer. Math. Soc. 328, 779–814.
Beerends, R. J. and Opdam, E. M. (1993). Certain hypergeometric series related to the root system BC, Trans. Amer. Math. Soc. 339, 581–609.
Berens, H., Schmid, H. and Xu, Y. (1995a). On two-dimensional definite orthogonal systems and on lower bound for the number of associated cubature formulas, SIAM J. Math. Anal. 26, 468–487.
Berens, H., Schmid, H. and Xu, Y. (1995b). Multivariate Gaussian cubature formula, Arch. Math. 64, 26–32.
Berens, H. and Xu, Y. (1996). Fejér means for multivariate Fourier series, Math. Z. 221, 449–465.
Berens, H. and Xu, Y. (1997). ℓ − 1 summability for multivariate Fourier integrals and positivity, Math. Proc. Cambridge Phil. Soc. 122, 149–172.
Berg, C. (1987). The multidimensional moment problem and semigroups, in Moments in Mathematics, pp. 110–124, Proceedings of Symposia in Applied Mathematics 37, American Mathemathical Society, Providence, RI.
Berg, C., Christensen, J. P. R. and Ressel, P. (1984). Harmonic Analysis on Semigroups, Theory of Positive Definite and Related Functions, Graduate Texts in Mathematics 100, Springer, New York–Berlin.
Berg, C. and Thill, M. (1991). Rotation invariant moment problems, Acta Math. 167, 207–227.
Bergeron, N. and Garsia, A. M. (1992). Zonal polynomials and domino tableaux, Discrete Math. 99, 3–15.
Bertran, M. (1975). Note on orthogonal polynomials in v-variables, SIAM. J. Math. Anal. 6, 250–257.
Bojanov, B. and Petrova, G. (1998). Numerical integration over a disc, a new Gaussian quadrature formula, Numer. Math. 80, 39–50.
Bos, L. (1994). Asymptotics for the Christoffel function for Jacobi like weights on a ball in ℝm, New Zealand J. Math. 23, 99–109.
Bos, L., Della Vecchia, B. and Mastroianni, G. (1998). On the asymptotics of Christoffel functions for centrally symmetric weights functions on the ball in ℝn, Rend. del Circolo Mat. di Palermo, 52, 277–290.
Bracciali, C. F., Delgado, A. M., Fernández, L., Pérez, T. E. and Piñar, M. A. (2010). New steps on Sobolev orthogonality in two variables, J. Comput. Appl. Math. 235, 916–926.
Braaksma, B. L. J. and Meulenbeld, B. (1968) Jacobi polynomials as spherical harmonics, Indag. Math. 30, 384–389.
Buchstaber, V., Felder, G. and Veselov, A. (1994). Elliptic Dunkl operators, root systems, and functional equations, Duke Math. J. 76, 885–891.
Calogero, F. (1971). Solution of the one-dimensional N-body problems with quadratic and/or inversely quadratic pair potentials, J. Math. Phys. 12, 419–436.
zu Castell, W., Filbir, F. and Xu, Y. (2009). Cesàro means of Jacobi expansions on the parabolic biangle, J. Approx. Theory 159, 167–179.
Cheney, E. W. (1998). Introduction to Approximation Theory, reprint of the 2nd edn (1982), AMS Chelsea, Providence, RI.
Cherednik, I. (1991). A unification of Knizhnik–Zamolodchikov and Dunkl operators via affine Hecke algebras, Invent. Math. 106, 411–431.
Chevalley, C. (1955). Invariants of finite groups generated by reflections, Amer. J. Math. 77, 777–782.
Chihara, T. S. (1978). An Introduction to Orthogonal Polynomials, Mathematics and its Applications 13, Gordon and Breach, New York.
Cichoń, D., Stochel, J. and Szafraniec, F. H. (2005). Three term recurrence relation modulo ideal and orthogonality of polynomials of several variables, J. Approx. Theory 134, 11–64.
Connett, W. C. and Schwartz, A. L. (1995). Continuous 2-variable polynomial hypergroups, in Applications of Hypergroups and Related Measure Algebras (Seattle, WA, 1993), pp. 89–109, Contemporary Mathematics 183, American Mathematical Society, Providence, RI.
van der Corput, J. G. and Schaake, G. (1935). Ungleichungen für Polynome und trigonometrische Polynome, Compositio Math. 2, 321–361.
Coxeter, H. S. M. (1935). The complete enumeration of finite groups of the form R2i = (RiRj)kij = 1, J. London Math. Soc. 10, 21–25.
Coxeter, H. S. M. (1973). Regular Polytopes, 3rd edn, Dover, New York.
Coxeter, H. S. M. and Moser, W. O. J. (1965). Generators and Relations for Discrete groups, 2nd edn, Springer, Berlin–New York.
Dai, F. and Wang, H. (2010). A transference theorem for the Dunkl transform and its applications, J. Funct. Anal. 258, 4052–4074.
Dai, F. and Xu, Y. (2009a). Cesàro means of orthogonal expansions in several variables, Const. Approx. 29, 129–155.
Dai, F. and Xu, Y. (2009b). Boundedness of projection operators and Cesàro means in weighted Lp space on the unit sphere, Trans. Amer. Math. Soc. 361, 3189–3221.
Dai, F. and Xu, Y. (2013). Approximation Theory and Harmonic Analysis on Spheres and Balls, Springer, Berlin–NewYork.
Debiard, A. and Gaveau, B. (1987). Analysis on root systems, Canad. J. Math. 39, 1281–1404.
Delgado, A. M., Fernández, L, Pérez, T. E., Piñar, M. A. and Xu, Y. (2010). Orthogonal polynomials in several variables for measures with mass points, Numer. Algorithm 55, 245–264.
Delgado, A., Geronimo, J. S., Iliev, P. and Marcellán, F. (2006). Two variable orthogonal polynomials and structured matrices, SIAM J. Matrix Anal. Appl. 28, 118–147.
Delgado, A. M., Geronimo, J. S., Iliev, P. and Xu, Y. (2009). On a two variable class of Bernstein–Szego measures, Constr. Approx. 30, 71–91.
DeVore, R. A. and Lorentz, G. G. (1993). Constructive approximation, Grundlehren der Mathematischen Wissenschaften 303, Springer, Berlin.
van Diejen, J. F. (1999). Properties of some families of hypergeometric orthogonal polynomials in several variables, Trans. Amer. Math. Soc. 351, no. 1, 233–270.
van Diejen, J. F. and Vinet, L. (2000). Calogero–Sutherland–Moser models, CRM Series in Mathematical Physics, Springer, New York.
Dieudonné, J. (1980). Special Functions and Linear Representations of Lie Groups, CBMS Regional Conference Series in Mathematics 42, American Mathematical Society, Providence, RI.
Dijksma, A. and Koornwinder, T. H. (1971). Spherical harmonics and the product of two Jacobi polynomials, Indag. Math. 33, 191–196.
Dubiner, M. (1991). Spectral methods on triangles and other domains, J. Sci. Comput. 6, 345–390.
Dunkl, C. F. (1981). Cube group invariant spherical harmonics and Krawtchouk polynomials, Math. Z. 92, 57–71.
Dunkl, C. F. (1982). An additional theorem for Heisenberg harmonics, in Proc. Conf. on Harmonic Analysis in Honor of Antoni Zygmund, pp. 688–705, Wadsworth International, Belmont, CA.
Dunkl, C. F. (1984a). The Poisson kernel for Heisenberg polynomials on the disk, Math. Z. 187, 527–547.
Dunkl, C. F. (1984b). Orthogonal polynomials with symmetry of order three, Canad. J. Math. 36, 685–717.
Dunkl, C. F. (1984c). Orthogonal polynomials on the sphere with octahedral symmetry, Trans. Amer. Math. Soc. 282, 555–575.
Dunkl, C. F. (1985). Orthogonal polynomials and a Dirichlet problem related to the Hilbert transform, Indag. Math. 47, 147–171.
Dunkl, C. F. (1986). Boundary value problems for harmonic functions on the Heisenberg group, Canad. J. Math. 38, 478–512.
Dunkl, C. F. (1987). Orthogonal polynomials on the hexagon, SIAM J. Appl. Math. 47, 343–351.
Dunkl, C. F. (1988). Reflection groups and orthogonal polynomials on the sphere, Math. Z. 197, 33–60.
Dunkl, C. F. (1989a). Differential–difference operators associated to reflection groups, Trans. Amer. Math. Soc. 311, 167–183.
Dunkl, C. F. (1989b). Poisson and Cauchy kernels for orthogonal polynomials with dihedral symmetry, J. Math. Anal. Appl. 143, 459–470.
Dunkl, C. F. (1990). Operators commuting with Coxeter group actions on polynomials, in Invariant Theory and Tableaux (Minneapolis, MN, 1988), pp. 107–117, IMA Mathematics and Applications 19, Springer, New York.
Dunkl, C. F. (1991). Integral kernels with reflection group invariance, Canad. J. Math. 43, 1213–1227.
Dunkl, C. F. (1992). Hankel transforms associated to finite reflection groups, in Hyper-geometric Functions on Domains of Positivity, Jack Polynomials, and Applications (Tampa, FL, 1991), pp. 123–138, Contemporary Mathematics 138, American Mathematical Society, Providence, RI.
Dunkl, C. F. (1995). Intertwining operators associated to the group S3, Trans. Amer. Math. Soc. 347, 3347–3374.
Dunkl, C. F. (1998a). Orthogonal polynomials of types A and B and related Calogero models, Comm. Math. Phys. 197, 451–487.
Dunkl, C. F. (1998b). Intertwining operators and polynomials associated with the symmetric group, Monatsh. Math. 126, 181–209.
Dunkl, C. F. (1999a). Computing with differential–difference operators, J. Symbolic Comput. 28, 819–826.
Dunkl, C. F. (1999b). Planar harmonic polynomials of type B, J. Phys. A: Math. Gen. 32, 8095–8110.
Dunkl, C. F. (1999c). Intertwining operators of type BN, in Algebraic Methods and q-Special Functions (Montréal, QC, 1996), pp. 119–134, CRM Proceedings Lecture Notes 22, American Mathematical Society, Providence, RI.
Dunkl, C. F. (2007). An intertwining operator for the group B2, Glasgow Math. J. 49, 291–319.
Dunkl, C. F., de Jeu, M. F. E. and Opdam, E. M. (1994). Singular polynomials for finite reflection groups, Trans. Amer. Math. Soc. 346, 237–256.
Dunkl, C. F. and Hanlon, P. (1998). Integrals of polynomials associated with tableaux and the Garsia–Haiman conjecture. Math. Z. 228, 537–567.
Dunkl, C. F. and Luque, J.-G. (2011). Vector-valued Jack polynomials from scratch, SIGMA 7, 026, 48pp.
Dunkl, C. F. and Opdam, E. M. (2003). Dunkl operators for complex reflection groups, Proc. London Math. Soc. 86, 70–108.
Dunkl, C. F. and Ramirez, D. E. (1971). Topics in Harmonic Analysis, Appleton-Century Mathematics Series, Appleton-Century-Crofts (Meredith Corporation), New York.
Dunn, K. B. and Lidl, R. (1982). Generalizations of the classical Chebyshev polynomials to polynomials in two variables, Czechoslovak Math. J. 32, 516–528.
Eier, R. and Lidl, R. (1974). Tschebyscheffpolynome in einer und zwei Variablen, Abh. Math. Sem. Univ. Hamburg 41, 17–27.
Eier, R. and Lidl, R. (1982). A class of orthogonal polynomials in k variables, Math. Ann. 260, 93–99.
Eier, R., Lidl, R. and Dunn, K. B. (1981). Differential equations for generalized Chebyshev polynomials, Rend. Mat. 1, no. 7, 633–646.
Engelis, G. K. (1974). Certain two-dimensional analogues of the classical orthogonal polynomials (in Russian), Latvian Mathematical Yearbook 15, 169–202, 235, Izdat. Zinatne, Riga.
Engels, H. (1980). Numerical Quadrature and Cubature, Academic Press, New York.
Erdélyi, A. (1965). Axially symmetric potentials and fractional integration, SIAM J. 13, 216–228.
Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G. (1953). Higher Transcendental Functions, McGraw-Hill, New York.
Etingof, E. (2010). A uniform proof of the Macdonald–Mehta–Opdam identity for finite Coxeter groups, Math. Res. Lett. 17, 277–284.
Exton, H. (1976). Multiple Hypergeometric Functions and Applications, Halsted, New York.
Fackerell, E. D. and Littler, R. A. (1974). Polynomials biorthogonal to Appell's polynomials, Bull. Austral. Math. Soc. 11, 181–195.
Farouki, R. T., Goodman, T. N. T. and Sauer, T. (2003). Construction of orthogonal bases for polynomials in Bernstein form on triangular and simplex domains, Comput. Aided Geom. Design 20, 209–230.
Fernández, L., Pérez, T. E. and Piñar, M. A. (2005). Classical orthogonal polynomials in two variables: a matrix approach, Numer. Algorithms 39, 131–142.
Fernández, L., Perez, T.E. and Piñar, M. A. (2011). Orthogonal polynomials in two variables as solutions of higher order partial differential equations, J. Approx. Theory 163, 84–97.
Folland, G. B. (1975). Spherical harmonic expansion of the Poisson–Szegő kernel for the ball, Proc. Amer. Math. Soc. 47, 401–408.
Forrester, P. J. and Warnaar, S. O. (2008). The importance of the Selberg integral Bull. Amer. Math. Soc. 45, 489–534.
Freud, G. (1966). Orthogonal Polynomials, Pergamon, New York.
Fuglede, B. (1983). The multidimensional moment problem, Expos. Math. 1, 47–65.
Gasper, G. (1972). Banach algebras for Jacobi series and positivity of a kernel, Ann. Math. 95, 261–280.
Gasper, G. (1977). Positive sums of the classical orthogonal polynomials, SIAM J. Math. Anal. 8, 423–447.
Gasper, G. (1981). Orthogonality of certain functions with respect to complex valued weights, Canad. J. Math. 33, 1261–1270.
Gasper, G. and Rahman, M. (1990). Basic Hypergeometric Series, Encyclopedia of Mathematics and its Applications 35, Cambridge University Press, Cambridge.
Gekhtman, M. I. and Kalyuzhny, A. A. (1994). On the orthogonal polynomials in several variables, Integr. Eq. Oper. Theory 19, 404–418.
Genest, V., Ismail, M., Vinet, L. and Zhedanov, A. (2013). The Dunkl oscillator in the plane I: superintegrability, separated wavefunctions and overlap coefficients, J. Phys. A: Math. Theor. 46, 145 201.
Genest, V., Vinet, L. and Zhedanov, A. (2013). The singular and the 2:1 anisotropic Dunkl oscillators in the plane, J. Phys. A: Math. Theor. 46, 325 201.
Ghanmi, A. (2008). A class of generalized complex Hermite polynomials, J. Math. Anal. Appl. 340, 1395–1406.
Ghanmi, A. (2013). Operational formulae for the complex Hermite polynomials Hp,q(z, z), Integral Transf. Special Func. 24, 884–895.
Görlich, E. and Markett, C. (1982). A convolution structure for Laguerre series, Indag. Math. 14, 161–171.
Griffiths, R. (1979). A transition density expansion for a multi-allele diffusion model. Adv. Appl. Prob. 11, 310–325.
Griffiths, R. and Spanò, D. (2011). Multivariate Jacobi and Laguerre polynomials, infinite-dimensional extensions, and their probabilistic connections with multivariate Hahn and Meixner polynomials, Bernoulli 17, 1095–1125.
Griffiths, R. and Spanò, D. (2013). Orthogonal polynomial kernels and canonical correlations for Dirichlet measures, Bernoulli 19, 548–598.
Groemer, H. (1996). Geometric Applications of Fourier Series and Spherical Harmonics, Cambridge University Press, New York.
Grove, L. C. (1974). The characters of the hecatonicosahedroidal group, J. Reine Angew. Math. 265, 160–169.
Grove, L. C. and Benson, C. T. (1985). Finite Reflection Groups, 2nd edn, Graduate Texts in Mathematics 99, Springer, Berlin-New York
Grundmann, A. and Möller, H. M. (1978). Invariant integration formulas for the n-simplex by combinatorial methods, SIAM. J. Numer. Anal. 15, 282–290.
Haviland, E. K. (1935). On the momentum problem for distributions in more than one dimension, I, II, Amer. J. Math. 57, 562–568; 58, 164–168.
Heckman, G. J. (1987). Root systems and hypergeometric functions II, Compositio Math. 64, 353–373.
Heckman, G. J. (1991a). A remark on the Dunkl differential–difference operators, in Harmonic Analysis on Reductive Groups (Brunswick, ME, 1989), pp. 181–191, Progress in Mathematics 101, Birkhauser, Boston, MA.
Heckman, G. J. (1991b). An elementary approach to the hypergeometric shift operators of Opdam, Invent. Math. 103, 341–350.
Heckman, G. J. and Opdam, E. M. (1987). Root systems and hypergeometric functions, I, Compositio Math. 64, 329–352.
Helgason, S. (1984). Groups and Geometric Analysis, Academic Press, New York.
Higgins, J. R. (1977). Completeness and Basis Properties of Sets of Special Functions, Cambridge University Press, Cambridge.
Hoffman, M. E. and Withers, W. D. (1988). Generalized Chebyshev polynomials associated with affine Weyl groups, Trans. Amer. Math. Soc. 308, 91–104.
Horn, R. A. and Johnson, C. R. (1985). Matrix Analysis, Cambridge University Press, Cambridge.
Hua, L. K. (1963). Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains, Translations of Mathematical Monographs 6, American Mathematical Society, Providence, RI.
Humphreys, J. E. (1990). Reflection Groups and Coxeter Groups, Cambridge Studies in Advanced Mathematics 29, Cambridge University Press, Cambridge.
Ignatenko, V. F. (1984). On invariants of finite groups generated by reflections, Math. USSRSb. 48, 551–563.
Ikeda, M. (1967). On spherical functions for the unitary group, I, II, III, Mem. Fac. Engrg Hiroshima Univ. 3, 17–75.
Iliev, P. (2011). Krall–Jacobi commutative algebras of partial differential operators, J. Math. Pures Appl. 96, no. 9, 446–461.
Intissar, A. and Intissar, A. (2006). Spectral properties of the Cauchy transform on L2(ℂ;e|z|2dλ), J. Math. Anal. Appl. 313, 400–418.
Ismail, M. (2005). Classical and Quantum Orthogonal Polynomials in One Variable, Encyclopedia of Mathematics and its Applications 71, Cambridge University Press, Cambridge.
Ismail, M. (2013). Analytic properties of complex Hermite polynomials. Trans. Amer. Math. Soc., to appear.
Ismail, M. and P., Simeonov (2013). Complex Hermite polynomials: their combinatorics and integral operators. Proc. Amer. Math. Soc., to appear.
Itô, K. (1952). Complex multiple Wiener integral, Japan J. Math. 22, 63–86.
Ivanov, K., Petrushev, P. and Xu, Y. (2010). Sub-exponentially localized kernels and frames induced by orthogonal expansions. Math. Z. 264, 361–397.
Ivanov, K., Petrushev, P. and Xu, Y. (2012). Decomposition of spaces of distributions induced by tensor product bases, J. Funct. Anal. 263, 1147–1197.
Jack, H. (1970/71). A class of symmetric polynomials with a parameter, Proc. Roy. Soc. Edinburgh Sect. A. 69, 1–18.
Jackson, D. (1936). Formal properties of orthogonal polynomials in two variables, Duke Math. J. 2, 423–434.
James, A. T. and Constantine, A. G. (1974). Generalized Jacobi polynomials as spherical functions of the Grassmann manifold, Proc. London Math. Soc. 29, 174–192.
de Jeu, M. F. E. (1993). The Dunkl transform, Invent. Math. 113, 147–162.
Kakei, S. (1998). Intertwining operators for a degenerate double affine Hecke algebra and multivariable orthogonal polynomials, J. Math. Phys. 39, 4993–5006.
Kalnins, E. G., Miller, W., Jr and Tratnik, M. V. (1991). Families of orthogonal and biorthogonal polynomials on the n-sphere, SIAM J. Math. Anal. 22, 272–294.
Kanjin, Y. (1985). Banach algebra related to disk polynomials, Tôhoku Math. J. 37, 395–404.
Karlin, S. and McGregor, J. (1962). Determinants of orthogonal polynomials, Bull. Amer. Math. Soc. 68, 204–209.
Karlin, S. and McGregor, J. (1975). Some properties of determinants of orthogonal polynomials, in Theory and Application of Special Functions, ed. R. A., Askey, pp. 521–550, Academic Press, New York.
Kato, Y. and Yamamoto, T. (1998). Jack polynomials with prescribed symmetry and hole propagator of spin Calogero–Sutherland model, J. Phys. A, 31, 9171–9184.
Kerkyacharian, G., Petrushev, P., Picard, D. and Xu, Y. (2009). Decomposition of Triebel–Lizorkin and Besov spaces in the context of Laguerre expansions, J. Funct. Anal. 256, 1137–1188.
Kim, Y. J., Kwon, K. H. and Lee, J. K. (1998). Partial differential equations having orthogonal polynomial solutions, J. Comput. Appl. Math. 99, 239–253.
Knop, F. and Sahi, S (1997). A recursion and a combinatorial formula for Jack polynomials. Invent. Math. 128, 9–22.
Koelink, E. (1996). Eight lectures on quantum groups and q-special functions, Rev. Colombiana Mat. 30, 93–180.
Kogbetliantz, E. (1924). Recherches sur la sommabilité des séries ultrasphériques par la méthode des moyennes arithmétiques, J. Math. Pures Appl. 3, no. 9, 107–187.
Koornwinder, T. H. (1974a). Orthogonal polynomials in two variables which are eigen-functions of two algebraically independent partial differential operators, I, II, Proc. Kon. Akad. v. Wet., Amsterdam 36, 48–66.
Koornwinder, T. H. (1974b). Orthogonal polynomials in two variables which are eigen-functions of two algebraically independent partial differential operators, III, IV, Proc. Kon. Akad. v. Wet., Amsterdam 36, 357–381.
Koornwinder, T. H. (1975). Two-variable analogues of the classical orthogonal polynomials, in Theory and Applications of Special Functions, ed. R. A., Askey pp. 435–495, Academic Press, New York.
Koornwinder, T. H. (1977). Yet another proof of the addition formula for Jacobi polynomials, J. Math. Anal. Appl. 61, 136–141.
Koornwinder, T. H. (1992). Askey-Wilson polynomials for root systems of type BC, in Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications, pp. 189–204, Contemporary Mathematics 138, American Mathematical Society, Providence, RI.
Koornwinder, T. H. and Schwartz, A. L. (1997). Product formulas and associated hypergroups for orthogonal polynomials on the simplex and on a parabolic biangle, Constr. Approx. 13, 537–567.
Koornwinder, T. H. and Sprinkhuizen-Kuyper, I. (1978). Generalized power series expansions for a class of orthogonal polynomials in two variables, SIAM J. Math. Anal. 9, 457–483.
Kowalski, M. A. (1982a). The recursion formulas for orthogonal polynomials in n variables, SIAM J. Math. Anal. 13, 309–315.
Kowalski, M. A. (1982b). Orthogonality and recursion formulas for polynomials in n variables, SIAM J. Math. Anal. 13, 316–323.
Krall, H. L. and Sheffer, I. M. (1967). Orthogonal polynomials in two variables, Ann. Mat. Pura Appl. 76, no. 4, 325–376.
Kroó, A. and Lubinsky, D. (2013a). Christoffel functions and universality on the boundary of the ball, Acta Math. Hungarica 140, 117–133.
Kroó, A. and Lubinsky, D. (2013b). Christoffel functions and universality in the bulk for multivariate orthogonal polynomials, Can. J. Math. 65, 600–620.
Kwon, K. H., Lee, J. K. and Littlejohn, L. L. (2001). Orthogonal polynomial eigenfunctions of second-order partial differential equations, Trans. Amer. Math. Soc. 353, 3629–3647.
Lapointe, L. and Vinet, L. (1996). Exact operator solution of the Calogero-Sutherland model, Comm. Math. Phys. 178, 425–452.
Laporte, O. (1948). Polyhedral harmonics, Z. Naturforschung 3a, 447–456.
Larcher, H. (1959). Notes on orthogonal polynomials in two variables. Proc. Amer. Math. Soc. 10, 417–423.
Lassalle, M. (1991a). Polynômes de Hermite généralisé (in French)C. R. Acad. Sci. Paris Sér. I Math. 313, 579–582.
Lassalle, M. (1991b). Polynômes de Jacobi généralisé (in French)C. R. Acad. Sci. Paris Sér. I Math. 312, 425–428.
Lassalle, M. (1991c). Polynômes de Laguerre généralisé (in French)C. R. Acad. Sci. Paris Sér. I Math. 312, 725–728.
Lasserre, J. (2012). The existence of Gaussian cubature formulas, J. Approx. Theory, 164, 572–585.
Lebedev, N. N. (1972). Special Functions and Their Applications, revised edn, Dover, New York.
Lee J. K.Littlejohn, L. L. (2006). Sobolev orthogonal polynomials in two variables and second order partial differential equations, J. Math. Anal. Appl. 322, 1001–1017.
Li, H., Sun, J. and Xu, Y. (2008). Discrete Fourier analysis, cubature and interpolation on a hexagon and a triangle, SIAM J. Numer. Anal. 46, 1653–1681.
Li, H. and Xu, Y. (2010). Discrete Fourier analysis on fundamental domain and simplex of Ad lattice in d-variables, J. Fourier Anal. Appl. 16, 383–433.
Li, Zh.-K. and Xu, Y. (2000). Summability of product Jacobi expansions, J. Approx. Theory 104, 287–301.
Li, Zh.-K. and Xu, Y. (2003). Summability of orthogonal expansions, J. Approx. Theory, 122, 267–333.
Lidl, R. (1975). Tschebyscheff polynome in mehreren variabelen, J. Reine Angew. Math. 273, 178–198.
Littlejohn, L. L. (1988). Orthogonal polynomial solutions to ordinary and partial differential equations, in Orthogonal Polynomials and Their Applications (Segovia, 1986), Lecture Notes in Mathematics 1329, 98–124, Springer, Berlin.
Logan, B. and Shepp, I. (1975). Optimal reconstruction of a function from its projections, Duke Math. J. 42, 649–659.
Lorentz, G. G. (1986). Approximation of Functions, 2nd edn, Chelsea, New York.
Lyskova, A. S. (1991). Orthogonal polynomials in several variables, Dokl. Akad. Nauk SSSR 316, 1301–1306; translation in Soviet Math. Dokl. 43 (1991), 264–268.
Macdonald, I. G. (1982). Some conjectures for root systems, SIAM, J. Math. Anal. 13, 988–1007.
Macdonald, I. G. (1995). Symmetric Functions and Hall Polynomials, 2nd edn, Oxford University Press, New York.
Macdonald, I. G. (1998). Symmetric Functions and Orthogonal Polynomials, University Lecture Series 12, American Mathematical Society, Providence, RI.
Maiorov, V. E. (1999). On best approximation by ridge functions, J. Approx. Theory 99, 68–94.
Markett, C. (1982). Mean Cesàro summability of Laguerre expansions and norm estimates with shift parameter, Anal. Math. 8, 19–37.
Marr, R. (1974). On the reconstruction of a function on a circular domain from a sampling of its line integrals, J. Math. Anal. Appl., 45, 357–374.
Máté, A., Nevai, P. and Totik, V. (1991). Szegő's extremum problem on the unit circle, Ann. Math. 134, 433–453.
Mehta, M. L. (1991). Random Matrices, 2nd edn, Academic Press, Boston, MA.
Möller, H. M. (1973). Polynomideale und Kubaturformeln, Thesis, University of Dort-mund.
Möller, H. M. (1976). Kubaturformeln mit minimaler Knotenzahl, Numer. Math. 25, 185–200.
Moody, R. and Patera, J. (2011). Cubature formulae for orthogonal polynomials in terms of elements of finite order of compact simple Lie groups, Adv. Appl. Math. 47, 509–535.
Morrow, C. R. and Patterson, T. N. L. (1978). Construction of algebraic cubature rules using polynomial ideal theory, SIAM J. Numer. Anal. 15, 953–976.
Müller, C. (1997). Analysis of Spherical Symmetries in Euclidean Spaces, Springer, New York.
Mysovskikh, I. P. (1970). A multidimensional analog of quadrature formula of Gaussian type and the generalized problem of Radon (in Russian), Vopr. Vychisl. i Prikl. Mat., Tashkent 38, 55–69.
Mysovskikh, I. P. (1976). Numerical characteristics of orthogonal polynomials in two variables, Vestnik Leningrad Univ. Math. 3, 323–332.
Mysovskikh, I. P. (1981). Interpolatory Cubature Formulas, Nauka, Moscow.
Narcowich, F. J., Petrushev, P, and Ward, J. D. (2006) Localized tight frames on spheres, SIAM J. Math. Anal. 38, 574–594.
Nelson, E. (1959). Analytic vectors, Ann. Math. 70, no. 2, 572–615.
Nevai, P. (1979). Orthogonal polynomials, Mem. Amer. Math. Soc. 18, no. 213.
Nevai, P. (1986). Géza Freud, orthogonal polynomials and Christoffel functions. A case study, J. Approx. Theory 48, 3–167.
Nesterenko, M., Patera, J., Szajewska, M. and Tereszkiewicz, A. (2010). Orthogonal polynomials of compact simple Lie groups: branching rules for polynomials, J. Phys. A 43, no. 49, 495 207, 27 pp.
Nishino, A., Ujino, H. and Wadati, M. (1999). Rodrigues formula for the nonsymmetric multivariable Laguerre polynomial, J. Phys. Soc. Japan 68, 797–802.
Noumi, M. (1996). Macdonald's symmetric polynomials as zonal spherical functions on some quantum homogeneous spaces, Adv. Math. 123, 16–77.
Nussbaum, A. E. (1966). Quasi-analytic vectors, Ark. Mat. 6, 179–191.
Okounkov, A. and Olshanski, G. (1998). Asymptotics of Jack polynomials as the number of variables goes to infinity, Int. Math. Res. Not. 13, 641–682.
Opdam, E. M. (1988). Root systems and hypergeometric functions, III, IV, Compositio Math. 67, 21–49, 191–209.
Opdam, E. M. (1991). Some applications of hypergeometric shift operators, Invent. Math. 98, 1–18.
Opdam, E. M. (1995). Harmonic analysis for certain representations of graded Hecke algebras, Acta Math. 175, 75–121.
Pérez, T.E., Piñar, M. A. and Xu, Y. (2013). Weighted Sobolev orthogonal polynomials on the unit ball, J. Approx. Theory, 171, 84–104.
Petrushev, P. (1999). Approximation by ridge functions and neural networks, SIAM J. Math. Anal. 30, 155–189.
Petrushev, P. and Xu, Y. (2008a). Localized polynomial frames on the ball, Constr. Approx. 27, 121–148.
Petrushev, P. and Xu, Y. (2008b). Decomposition of spaces of distributions induced by Hermite expansions, J. Fourier Anal. Appl. 14, 372–414.
Piñar, M. and Xu, Y. (2009). Orthogonal polynomials and partial differential equations on the unit ball, Proc. Amer. Math. Soc. 137, 2979–2987.
Podkorytov, A. M. (1981). Summation of multiple Fourier series over polyhedra, Vestnik Leningrad Univ. Math. 13, 69–77.
Proriol, J. (1957). Sur une famille de polynomes à deux variables orthogonaux dans un triangle, C. R. Acad. Sci. Paris 245, 2459–2461.
Putinar, M. (1997). A dilation theory approach to cubature formulas, Expos. Math. 15, 183–192.
Putinar, M. (2000). A dilation theory approach to cubature formulas II, Math. Nach. 211, 159–175.
Putinar, M. and Vasilescu, F. (1999). Solving moment problems by dimensional extension, Ann. Math. 149, 1087–1107.
Radon, J. (1948). Zur mechanischen Kubatur, Monatsh. Math. 52, 286–300.
Reznick, B. (2000). Some concrete aspects of Hilbert's 17th problem, in Real Algebraic Geometry and Ordered Structures, pp. 251–272, Contemporary Mathematics 253, American Mathematical Society, Providence, RI.
Ricci, P. E. (1978). Chebyshev polynomials in several variables (in Italian), Rend. Mat. 11, no. 6, 295–327.
Riesz, F. and Sz., Nagy, B. (1955). Functional Analysis, Ungar, NewYork.
Rosengren, H. (1998). Multilinear Hankel forms of higher order and orthogonal polynomials, Math. Scand. 82, 53–88.
Rosengren, H. (1999). Multivariable orthogonal polynomials and coupling coefficients for discrete series representations, SIAM J. Math. Anal. 30, 232–272.
Rosier, M. (1995). Biorthogonal decompositions of the Radon transform, Numer. Math. 72, 263–283.
Rösler, M. (1998). Generalized Hermite polynomials and the heat equation for Dunkl operators, Comm. Math. Phys. 192, 519–542.
Rösler, M. (1999). Positivity of Dunkl's intertwining operator, Duke Math. J., 98, 445–463.
Rösler, M. and Voit, M. (1998). Markov processes related with Dunkl operators. Adv. Appl. Math. 21, 575–643.
Rozenblyum, A. V. and Rozenblyum, L. V. (1982). A class of orthogonal polynomials of several variables, Differential Eq. 18, 1288–1293.
Rozenblyum, A. V. and Rozenblyum, L. V. (1986). Orthogonal polynomials of several variables, which are connected with representations of groups of Euclidean motions, Differential Eq. 22, 1366–1375.
Rudin, W. (1991). Functional Analysis, 2nd edn., International Series in Pure and Applied Mathematics, McGraw-Hill, New York.
Sahi, S. (1996). A new scalar product for nonsymmetric Jack polynomials, Int. Math. Res. Not. 20, 997–1004.
Schmid, H. J. (1978). On cubature formulae with a minimum number of knots, Numer. Math. 31, 281–297.
Schmid, H. J. (1995). Two-dimensional minimal cubature formulas and matrix equations, SIAM J. Matrix Anal. Appl. 16, 898–921.
Schmid, H. J. and Xu, Y. (1994). On bivariate Gaussian cubature formula, Proc. Amer. Math. Soc. 122, 833–842.
Schmüdgen, K. (1990). Unbounded Operator Algebras and Representation Theory, Birkhäuser, Boston, MA.
Selberg, A. (1944). Remarks on a multiple integral (in Norwegian), Norsk Mat. Tidsskr.26, 71–78.
Shephard, G. C. and Todd, J. A. (1954). Finite unitary reflection groups, Canad. J. Math. 6, 274–304.
Shishkin, A. D. (1997). Some properties of special classes of orthogonal polynomials in two variables, Integr. Transform. Spec. Funct. 5, 261–272.
Shohat, J. and Tamarkin, J. (1943). The Problem of Moments, Mathematics Surveys 1, American Mathematical Society, Providence, RI.
Sprinkhuizen-Kuyper, I. (1976). Orthogonal polynomials in two variables. A further analysis of the polynomials orthogonal over a region bounded by two lines and a parabola, SIAM J. Math. Anal. 7, 501–518.
Stanley, R. P. (1989). Some combinatorial properties of Jack symmetric functions, Adv. Math. 77, 76–115.
Stein, E. M. (1970). Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, NJ.
Stein, E. M. and Weiss, G. (1971). Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, NJ.
Stokman, J. V. (1997). Multivariable big and little q-Jacobi polynomials, SIAM J. Math. Anal. 28, 452–480.
Stokman, J. V. and Koornwinder, T. H. (1997). Limit transitions for BC type multivariable orthogonal polynomials, Canad. J. Math. 49, 373–404.
Stroud, A. (1971). Approximate Calculation of Multiple Integrals, Prentice-Hall, Englewood Cliffs, NJ.
Suetin, P. K. (1999). Orthogonal Polynomials in Two Variables, translated from the 1988 Russian original by E. V. Pankratiev, Gordon and Breach, Amsterdam.
Sutherland, B. (1971). Exact results for a quantum many-body problem in one dimension, Phys. Rev. A 4, 2019–2021.
Sutherland, B. (1972). Exact results for a quantum many-body problem in one dimension, II, Phys. Rev. A 5, 1372–1376.
Szegő, G. (1975). Orthogonal Polynomials, 4th edn, American Mathematical Society Colloquium Publication 23, American Mathematical Society, Providence, RI.
Thangavelu, S. (1992). Transplantaion, summability and multipliers for multiple Laguerre expansions, Tôhoku Math. J. 44, 279–298.
Thangavelu, S. (1993). Lectures on Hermite and Laguerre Expansions, Princeton University Press, Princeton, NJ.
Thangavelu, S. and Xu, Y. (2005). Convolution operator and maximal function for the Dunkl transform, J. Anal. Math. 97, 25–55.
Tratnik, M.V. (1991a). Some multivariable orthogonal polynomials of the Askey tableau – continuous families, J. Math. Phys. 32, 2065–2073.
Tratnik, M.V. (1991b). Some multivariable orthogonal polynomials of the Askey tableau – discrete families, J. Math. Phys. 32, 2337–2342.
Uglov, D. (2000). Yangian Gelfand–Zetlin bases, glN-Jack polynomials, and computation of dynamical correlation functions in the spin Calogero–Sutherland model, in Calogero–Sutherland–Moser Models, pp. 485–495, CRM Series in Mathematical Physics, Springer, New York.
Ujino, H. and Wadati, M. (1995). Orthogonal symmetric polynomials associated with the quantum Calogero model, J. Phys. Soc. Japan 64, 2703–2706.
Ujino, H. and Wadati, M. (1997). Orthogonality of the Hi-Jack polynomials associated with the Calogero model, J. Phys. Soc. Japan 66, 345–350.
Ujino, H. and Wadati, M. (1999). Rodrigues formula for the nonsymmetric multivariable Hermite polynomial, J. Phys. Soc. Japan 68, 391–395.
Verlinden, P. and Cools, R. (1992). On cubature formulae of degree 4k + 1 attaining Möller's lower bound for integrals with circular symmetry, Numer. Math. 61, 395–407.
Vilenkin, N. J. (1968). Special Functions and the Theory of Group Representations, American Mathematical Society Translation of Mathematics Monographs 22, American Mathematical Society, Providence, RI.
Vilenkin, N. J. and Klimyk, A. U. (1991a). Representation of Lie Groups and Special Functions. Vol. 1. Simplest Lie Groups, Special Functions and Integral Transforms, Mathematics and its Applications (Soviet Series) 72, Kluwer, Dordrecht.
Vilenkin, N. J. and Klimyk, A. U. (1991b). Representation of Lie Groups and Special Functions. Vol. 2. Class I Representations, Special Functions, and Integral Transforms, Mathematics and its Applications (Soviet Series) 72, Kluwer, Dordrecht, Netherlands.
Vilenkin, N. J. and Klimyk, A. U. (1991c). Representation of Lie Groups and Special Functions. Vol. 3. Classical and Quantum Groups and Special Functions, Mathematics and its Applications (Soviet Series) 72, Kluwer, Dordrecht, Netherlands.
Vilenkin, N. J. and Klimyk, A. U. (1995). Representation of Lie Groups and Special Functions. Recent Advances, Mathematics and its Applications 316, Kluwer, Dordrecht, Netherlands.
Volkmer, H. (1999). Expansions in products of Heine–Stieltjes polynomials, Constr. Approx. 15, 467–480.
Vretare, L. (1984). Formulas for elementary spherical functions and generalized Jacobi polynomials, SIAM. J. Math. Anal. 15, 805–833.
Wade, J. (2010). A discretized Fourier orthogonal expansion in orthogonal polynomials on a cylinder, J. Approx. Theory 162, 1545–1576.
Wade, J. (2011). Cesàro summability of Fourier orthogonal expansions on the cylinder, J. Math. Anal. Appl. 402 (2013), 446–452.
Waldron, S. (2006). On the Bernstein–Bézier form of Jacobi polynomials on a simplex, J. Approx. Theory 140, 86–99.
Waldron, S. (2008). Orthogonal polynomials on the disc, J. Approx. Theory 150, 117–131.
Waldron, S. (2009). Continuous and discrete tight frames of orthogonal polynomials for a radially symmetric weight. Constr. Approx. 30, 3352.
Wünsche, A. (2005). Generalized Zernike or disc polynomials, J. Comp. Appl. Math. 174, 135–163.
Xu, Y. (1992). Gaussian cubature and bivariable polynomial interpolation, Math. Comput. 59, 547–555.
Xu, Y. (1993a). On multivariate orthogonal polynomials, SIAM J. Math. Anal. 24, 783–794.
Xu, Y. (1993b). Unbounded commuting operators and multivariate orthogonal polynomials, Proc. Amer. Math. Soc. 119, 1223–1231.
Xu, Y. (1994a). Multivariate orthogonal polynomials and operator theory, Trans. Amer. Math. Soc. 343, 193–202.
Xu, Y. (1994b). Block Jacobi matrices and zeros of multivariate orthogonal polynomials, Trans. Amer. Math. Soc. 342, 855–866.
Xu, Y. (1994c). Recurrence formulas for multivariate orthogonal polynomials, Math. Comput. 62, 687–702.
Xu, Y. (1994d). On zeros of multivariate quasi-orthogonal polynomials and Gaussian cubature formulae, SIAM J. Math. Anal. 25, 991–1001.
Xu, Y. (1994e). Solutions of three-term relations in several variables, Proc. Amer. Math. Soc. 122, 151–155.
Xu, Y. (1994f). Common Zeros of Polynomials in Several Variables and Higher Dimensional Quadrature, Pitman Research Notes in Mathematics Series 312, Longman, Harlow.
Xu, Y. (1995). Christoffel functions and Fourier series for multivariate orthogonal polynomials, J. Approx. Theory 82, 205–239.
Xu, Y. (1996a). Asymptotics for orthogonal polynomials and Christoffel functions on a ball, Meth. Anal. Appl. 3, 257–272.
Xu, Y. (1996b). Lagrange interpolation on Chebyshev points of two variables, J. Approx. Theory 87, 220–238.
Xu, Y. (1997a). On orthogonal polynomials in several variables, in Special Functions, q-Series and Related Topics, pp. 247–270, The Fields Institute for Research in Mathematical Sciences, Communications Series 14, American Mathematical Society, Providence, RI.
Xu, Y. (1997b). Orthogonal polynomials for a family of product weight functions on the spheres, Canad. J. Math. 49, 175–192.
Xu, Y. (1997c). Integration of the intertwining operator for h-harmonic polynomials associated to reflection groups, Proc. Amer. Math. Soc. 125, 2963–2973.
Xu, Y. (1998a). Intertwining operator and h-harmonics associated with reflection groups, Canad. J. Math. 50, 193–209.
Xu, Y. (1998b). Orthogonal polynomials and cubature formulae on spheres and on balls, SIAM J. Math. Anal. 29, 779–793.
Xu, Y. (1998c). Orthogonal polynomials and cubature formulae on spheres and on simplices, Meth. Anal. Appl. 5, 169–184.
Xu, Y. (1998d). Summability of Fourier orthogonal series for Jacobi weight functions on the simplex in ℝd, Proc. Amer. Math. Soc. 126, 3027–3036.
Xu, Y. (1999a). Summability of Fourier orthogonal series for Jacobi weight on a ball in ℝd, Trans. Amer. Math. Soc. 351, 2439–2458.
Xu, Y. (1999b). Aymptotics of the Christoffel functions on a simplex in ℝd, J. Approx. Theory 99, 122–133.
Xu, Y. (1999c). Cubature formulae and polynomial ideals, Adv. Appl. Math. 23, 211–233.
Xu, Y. (2000a). Harmonic polynomials associated with reflection groups, Canad. Math. Bull. 43, 496–507.
Xu, Y. (2000b). Funk-Hecke formula for orthogonal polynomials on spheres and on balls, Bull. London Math. Soc. 32, 447–457.
Xu, Y. (2000c). Constructing cubature formulae by the method of reproducing kernel, Numer. Math. 85, 155–173.
Xu, Y. (2000d). A note on summability of Laguerre expansions, Proc. Amer. Math. Soc. 128, 3571–3578.
Xu, Y. (2000e). A product formula for Jacobi polynomials, in Special Functions (Hong Kong, 1999), pp. 423–430, World Science, River Edge, NJ.
Xu, Y. (2001a). Orthogonal polynomials and summability in Fourier orthogonal series on spheres and on balls, Math. Proc. Cambridge Phil. Soc. 31 (2001), 139–155.
Xu, Y. (2001b). Orthogonal polynomials on the ball and the simplex for weight functions with reflection symmetries, Constr. Approx. 17, 383–412.
Xu, Y. (2004). On discrete orthogonal polynomials of several variables, Adv. Appl. Math. 33, 615–632.
Xu, Y. (2005a). Weighted approximation of functions on the unit sphere, Constr. Approx. 21, 1–28.
Xu, Y. (2005b). Second order difference equations and discrete orthogonal polynomials of two variables, Int. Math. Res. Not. 8, 449–475.
Xu, Y. (2005c). Monomial orthogonal polynomials of several variables, J. Approx. Theory, 133, 1–37.
Xu, Y. (2005d). Rodrigues type formula for orthogonal polynomials on the unit ball, Proc. Amer. Math. Soc. 133, 1965–1976.
Xu, Y. (2006a). A direct approach to the reconstruction of images from Radon projections, Adv. Applied Math. 36, 388–420.
Xu, Y. (2006b). A family of Sobolev orthogonal polynomials on the unit ball, J. Approx. Theory 138, 232–241.
Xu, Y. (2006c). Analysis on the unit ball and on the simplex, Electron. Trans. Numer. Anal., 25, 284–301.
Xu, Y. (2007). Reconstruction from Radon projections and orthogonal expansion on a ball, J. Phys. A: Math. Theor. 40, 7239–7253.
Xu, Y. (2008). Sobolev orthogonal polynomials defined via gradient on the unit ball, J. Approx. Theory 152, 52–65.
Xu, Y. (2010). Fourier series and approximation on hexagonal and triangular domains, Const. Approx. 31, 115–138.
Xu, Y. (2012). Orthogonal polynomials and expansions for a family of weight functions in two variables. Constr. Approx. 36, 161–190.
Xu, Y. (2013). Complex vs. real orthogonal polynomials of two variables. Integral Transforms Spec. Funct., to appear. arXiv:1307.819.
Yamamoto, T. (1995). Multicomponent Calogero model of BN-type confined in a harmonic potential, Phys. Lett. A 208, 293–302.
Yan, Z. M. (1992). Generalized hypergeometric functions and Laguerre polynomials in two variables, in Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications, pp. 239–259, Contemporary Mathematics 138, American Mathematical Society, Providence, RI.
Zernike, F. and Brinkman, H. C. (1935). Hypersphärishe Funktionen und die in sphärischen Bereichen orthogonalen Polynome, Proc. Kon. Akad. v. Wet., Amsterdam 38, 161–170.
Zygmund, A. (1959). Trigonometric Series, Cambridge University Press, Cambridge.