Bibliography[1] L.W., Baggett, A weak containment theorem for groups with a quotient R-group. Trans. Amer. Math. Soc., 128 (1967), 277–90.
[2] L.W., Baggett, A description of the topology on the dual spaces of certain locally compact groups. Trans. Amer. Math. Soc., 132 (1968), 175–212.
[3] L.W., Baggett, A separable group having a discrete dual space is compact. J. Funct. Anal., 10 (1972), 131–48.
[4] L.W., Baggett, Representations of the Mautner group. I. Pacific J. Math., 77 (1978), 7–22.
[5] L.W., Baggett, On the continuity of Mackey's extension process. J. Funct. Anal., 56 (1984), 233–50.
[6] L.W., Baggett and A., Kleppner, Multiplier representations of abelian groups. J. Funct. Anal., 14 (1973), 299–324.
[7] L.W., Baggett and K., Merrill, Representations of theMautner group and cocycles of an irrational rotation. Michigan Math. J., 33 (1986), 221–9.
[8] L.W., Baggett and J., Packer, C*-algebras associated to two-step nilpotent groups. Contemporary Math., 120 (1991), 1–6.
[9] L.W., Baggett and J., Packer, The primitive ideal space of two-step nilpotent group C*-algebras. J. Funct. Anal., 124 (1994), 389–426.
[10] L.W., Baggett and A., Ramsay, Some pathologies in the Mackey analysis for a certain nonseparable group. J. Funct. Anal., 39 (1980), 375–80.
[11] L.W., Baggett and T., Sund, The Hausdorff dual problem for connected groups. J. Funct. Anal., 43 (1981), 60–8.
[12] L.W., Baggett and K.F., Taylor, Riemann–Lebesgue subsets of ℝn and representations which vanish at infinity. J. Funct. Anal., 28 (1978), 168–81.
[13] L.W., Baggett and K.F., Taylor, On asymptotic behaviour of induced representations. Canad. J. Math., 34 (1982), 220–32.
[14] B.A., Barnes, The role of minimal idempotents in the representation theory of locally compact groups. Proc. Edinb. Math. Soc., 23 (1980), 229–38.
[15] A.O., Barut and R., Raczka, Theory of Group Representations and Applications. Warsaw: Polish Scientific Publishers, 1977.
[16] M.E.B., Bekka, A characterization of locally compact amenable groups by means of tensor products. Arch. Math. (Basel), 52 (1989), 424–7.
[17] M.E.B., Bekka and R., Curtis, On Mackey's irreducibility criterion for induced representations. Int. Math. Res. Not., 38 (2003), 2095–101.
[18] M.E.B., Bekka and E., Kaniuth, Topological Frobenius properties for nilpotent groups. Math. Scand., 63 (1988), 282–96.
[19] D., Bernier and K.F., Taylor, Wavelets from square-integrable representations. SIAM J. Math. Anal., 27 (1996), 594–608.
[20] M.W., Binder, Irreducible induced representations of ICC groups. Math. Ann., 294 (1992), 37–47.
[21] M.W., Binder, On induced representations of discrete groups. Proc. Amer. Math. Soc., 118 (1993), 301–9.
[22] R.J., Blattner, On induced representations. Amer. J. Math., 83 (1961), 79–98.
[23] R.J., Blattner, On induced representations. II. Infinitesimal induction. Amer. J. Math., 83 (1961), 499–512.
[24] R.J., Blattner, On a theorem of G.W. Mackey. Bull. Amer. Math. Soc., 68 (1962), 585–7.
[25] R.J., Blattner, A theorem on induced representations. Proc. Amer. Math. Soc., 13 (1962), 881–4.
[26] R.J., Blattner, Positive definite measures. Proc. Amer. Math. Soc., 14 (1963), 423–8.
[27] R.J., Blattner, Group extension representations and the structure space. Pacific J. Math., 15 (1965), 1101–13.
[28] I.D., Brown, Dual topology of a nilpotent Lie group. Ann. Sci. Éc. Norm. Sup. (4), 6 (1973), 407–11.
[29] R.C., Busby and I.E., Schochetman, Compact induced representations. Canad. J. Math., 24 (1972), 5–16.
[30] R.C., Busby, I.E., Schochetman and H.A., Smith, Integral operators and the compactness of induced representations. Trans. Amer. Math. Soc., 164 (1972), 461–77.
[31] L., Corwin, Induced representations of discrete groups. Proc. Amer. Math. Soc., 47 (1975), 279–87.
[32] L., Corwin and F.P., Greenleaf, Intertwining operators for representations induced from uniform subgroups. Acta Math., 136 (1976), 275–301.
[33] L., Corwin and F.P., Greenleaf, Representations of Nilpotent Lie Groups and their Applications. Part 1: Basic Theory and Examples. Cambridge: Cambridge University Press, 1990.
[34] J., Dauns and K.H., Hofmann, Representations of rings by sections. Mem. Amer. Math. Soc., 83 (1968).
[35] J., Dixmier, Sur les représentations unitaires des groupes de Lie nilpotents. VI.Canad. J. Math., 12 (1960), 324–52.
[36] J., Dixmier, Les Algèbres d'Opérateurs dans l'Espace Hilbertien. Paris: Gauthier-Villars, 1969.
[37] J., Dixmier, C*-algebras. Amsterdam: North-Holland, 1977.
[38] S., Echterhoff, Mackey'sche Theorie irreduzibler Darstellungen und Topologie im Dual lokalkompakter Gruppen. Diplomarbeit, Universität Paderborn, 1986.
[39] R.C., Fabec, Fundamentals of Infinite Dimensional Representation Theory. Boca Raton, FL: Chapman and Hall/CRC, 2000.
[40] R.A., Fakler, On Mackey's tensor product theorem. Duke Math. J., 40 (1973), 689–94.
[41] R.A., Fakler, Erratum to “On Mackey's tensor product theorem”. Duke Math. J., 41 (1974), 691.
[42] R.A., Fakler, Representations induced from conjugate subgroups. Indiana J. Math., 19 (1977), 167–71.
[43] R.A., Fakler, An intertwining number theorem for induced representations. Nanta Math., 11 (1978), 164–73.
[44] R., Felix, Über Integralzerlegungen von Darstellungen nilpotenter Liegruppen. Manuscr. Math., 9 (1979), 279–90.
[45] R., Felix, R.W., Henrichs and H., Skudlarek, Topological Frobenius reciprocity for projective limits of Lie groups. Math. Z., 165 (1979), 19–28.
[46] J.M.G., Fell, The dual spaces of C*-algebras. Trans. Amer. Math. Soc., 94 (1960), 365–403.
[47] J.M.G., Fell, A new proof that nilpotent groups are CCR. Proc. Amer. Math. Soc., 13 (1962), 93–9.
[48] J.M.G., Fell, A Hausdorff topology on the closed subsets of a locally compact non-Hausdorff space. Proc. Amer. Math. Soc., 13 (1962), 472–6.
[49] J.M.G., Fell, Weak containment and induced representations of groups. Canad. J. Math., 14 (1962), 237–68.
[50] J.M.G., Fell, Weak containment andKronecker products of group representations. Pacific J. Math., 13 (1963), 503–10.
[51] J.M.G., Fell, Weak containment and induced representations of groups. II. Trans. Amer. Math. Soc., 110 (1964), 424–47.
[52] J.M.G., Fell, A new look at Mackey's imprimitivity theorem. In: Conference on Harmonic Analysis, Lecture Notes in Mathematics 266. Berlin: Springer-Verlag 1972, pp. 43–58.
[53] J.M.G., Fell and R.S., Doran, Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles, Vol. 1: Basic Representation Theory of Groups and Algebras. Boston: Academic Press, 1988.
[54] J.M.G., Fell and R.S., Doran, Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles, Vol. 2: Banach *-Algebraic Bundles, Induced Representations, and the Generalized Mackey Analysis. Boston: Academic Press, 1988.
[55] G.B., Folland, A Course in Abstract Harmonic Analysis. Boca Raton: CRC Press, 1995.
[56] F.G., Frobenius, Über Relationen zwischen den Charakteren einer Gruppe und denen ihrer Untergruppen. Sitz. Preuss. Akad.Wiss. (1898), 501–15; also pp. 104–18 in Frobenius's Gesammelte Abhandlungen, Vol. III. Berlin: Springer, 1968.
[57] S.A., Gaal, Linear Analysis and Representation Theory. GrundlehrenMath.Wiss. 198. Berlin: Springer, 1973.
[58] I.M., Gelfand and M.A., Naimark, On the embedding of normed rings into the ring of operators in Hilbert space. Mat. Sb. N. S., 12(54) (1943), 197–213.
[59] I.M., Gelfand and D.A., Raikov, Irreducible unitary representations of locally bicompact groups. Mat. Sb. N. S., 13(55) (1943), 301–16.
[60] J.G., Glimm, Locally compact transformation groups. Trans. Amer. Math. Soc., 101 (1961), 124–38.
[61] J.G., Glimm, Type I C*-algebras. Ann. of Math., 73 (1961), 572–612.
[62] J.G., Glimm, Families of induced representations. Pacific J. Math., 12 (1962), 885–911.
[63] R., Godement, Les fonctions de type positif et la thèorie des groupes. Trans. Amer. Math. Soc., 63 (1948), 1–84.
[64] E.C., Gootman, Weak containment and weak Frobenius reciprocity. Proc. Amer. Math. Soc., 54 (1976), 417–22.
[65] E.C., Gootman, Induced representations and finite volume homogeneous spaces. J. Funct. Anal., 24 (1977), 223–40.
[66] E.C., Gootman and J., Rosenberg, The structure of crossed product C*-algebras: a proof of the generalized Effros–Hahn conjecture. Invent. Math., 52 (1979), 283–98.
[67] F.P., Greenleaf, Invariant Means on Topological Groups. NewYork: van Nostrand, 1969.
[68] F.P., Greenleaf, Amenable actions of locally compact groups. J. Funct. Anal., 4 (1969), 295–315.
[69] K., Gröchenig, E., Kaniuth and K.F., Taylor, Compact open sets in duals and projections in L1-algebras of certain semi-direct product groups. Math. Proc. Cambridge Phil. Soc., 111 (1992), 545–56.
[70] S., Grosser and M., Moskowitz, Compactness conditions in topological groups. J. Reine Angew. Math., 246 (1971), 1–40.
[71] R.W., Henrichs, Die Frobeniuseigenschaft FP für diskrete Gruppen. Math. Z., 147 (1976), 191–9.
[72] R.W., Henrichs, Weak Frobenius reciprocity and compactness conditions in topological groups. Pacific J. Math., 82 (1979), 387–406.
[73] E., Hewitt and K.A., Ross, Abstract Harmonic Analysis. I. Berlin: Springer, 1963.
[74] E., Hewitt and K.A., Ross, Abstract Harmonic Analysis. II. Berlin: Springer, 1970.
[75] R.E., Howe, On representations of discrete, finitely generated, torsion-free, nilpotent groups. Pacific J. Math., 73 (1977), 281–305.
[76] R.E., Howe, The Fourier transform for nilpotent locally compact groups. Pacific J. Math., 73 (1977), 307–27.
[77] R.E., Howe and C.C., Moore, Asymptotic properties of unitary representations. J. Funct. Anal., 32 (1979), 72–96.
[78] A., Hulanicki, Groups whose regular representation weakly contains all unitary representations. Studia Math., 24 (1964), 37–59.
[79] R.V., Kadison and J.R., Ringrose, Fundamentals of the Theory of Operator Algebras. I. New York: Academic Press, 1983.
[80] R.V., Kadison and J.R., Ringrose, Fundamentals of the Theory of Operator Algebras. II. New York: Academic Press, 1986.
[81] E., Kaniuth, Primitive ideal spaces of groups with relatively compact conjugacy classes. Arch. Math. (Basel), 32 (1979), 16–24.
[82] E., Kaniuth, On primary ideals in group algebras. Monatsh. Math., 93 (1982), 293–302.
[83] E., Kaniuth, Weak containment and tensor products of group representations. II. Math. Ann., 270 (1985), 1–15.
[84] E., Kaniuth, On topological Frobenius reciprocity for locally compact groups. Arch. Math. (Basel), 48 (1987), 286–97.
[85] E., Kaniuth, Topological Frobenius properties for nilpotent groups. II. Math. Scand., 68 (1991), 89–107.
[86] E., Kaniuth, A Course in Commutative Banach Algebras. Graduate Texts in Mathematics 246. New York: Springer, 2009.
[87] E., Kaniuth and W., Moran, The Glimm ideal space of a two-step nilpotent locally compact group. Proc. Edinb. Math. Soc., 44 (2001), 505–26.
[88] E., Kaniuth and K.F., Taylor, Minimal projections in L1-algebras and open points in the dual spaces of semi-direct product groups. J. London Math. Soc., 53 (1996), 141–57.
[89] A., Kleppner, On the intertwining number theorem. Proc. Amer. Math. Soc., 12 (1961), 731–3.
[90] A., Kleppner, The structure of some induced representations. Duke Math. J., 29 (1962), 555–72.
[91] A., Kleppner, Multipliers on abelian groups. Math. Ann., 158 (1965), 11–34.
[92] A., Kleppner, Representations induced from compact subgroups. Amer. J. Math., 88 (1966), 544–52.
[93] A.W., Knapp, Representation Theory of Semisimple Groups: An Overview Based on Examples. Princeton, NJ: Princeton University Press, 1986.
[94] R.A., Kunze, On the Frobenius reciprocity theorem for square-integrable representations. Pacific J. Math., 53 (1974), 465–71.
[95] G., Kutyniok and D., Labate, Resolution of the wavefront set using continuous shearlets. Trans. Amer. Math. Soc., 361 (2009), 2719–54.
[96] R.L., Lipsman, Group Representations. Lecture Notes in Mathematics 388. Berlin: Springer, 1974.
[97] J.R., Liukkonen and R.D., Mosak, The primitive dual space of [FC]− -groups. J. Funct. Anal., 15 (1974), 279–96.
[98] L.H., Loomis, Positive definite functions and induced representations. Duke Math. J., 27 (1960), 569–79.
[99] G.W., Mackey, Imprimitivity for representations of locally compact groups. I.Proc. Nat. Acad. Sci. USA, 35 (1949), 537–45.
[100] G.W., Mackey, On induced representations of groups. Amer. J. Math., 73 (1951), 576–92.
[101] G.W., Mackey, Induced representations of locally compact groups. I. Ann. of Math., 55 (1952), 101–39.
[102] G.W., Mackey, Induced representations of locally compact groups. II: The Frobenius theorem. Ann. of Math., 58 (1953), 193–220.
[103] G.W., Mackey, Unitary representations of group extensions. I. Acta Math., 99 (1958), 265–311.
[104] G.W., Mackey, Induced Representations of Groups and Quantum Mechanics. New York: Benjamin, 1968.
[105] G.W., Mackey, The Theory of Unitary Group Representations. Chicago: The University of Chicago Press, 1976.
[106] G.W., Mackey, Unitary Group Representations in Physics, Probability, and Number Theory. Mathematics Lecture Note Series 55. Reading, MA: Benjamin/Cummings, 1978.
[107] F.I., Mautner, Unitary representations of locally compact groups. II. Ann. of Math., 52 (1950), 528–56.
[108] F.I., Mautner, A generalization of the Frobenius reciprocity theorem. Proc. Nat. Acad. Sci. USA, 37 (1951), 431–5.
[109] F.I., Mautner, Induced representations. Amer. J. Math., 74 (1952), 737–58.
[110] C.C., Moore, On the Frobenius reciprocity theorem for locally compact groups. Pacific J. Math., 12 (1962), 359–65.
[111] C.C., Moore, Groups with finite dimensional irreducible representations. Trans. Amer. Math. Soc., 166 (1972), 401–10.
[112] C.C., Moore and J., Repka, A reciprocity theorem for tensor products of group representations. Proc. Amer. Math. Soc., 64 (1977), 361–4.
[113] C.C., Moore and J.A., Wolf, Square integrable representations of nilpotent Lie groups. Trans. Amer. Math. Soc., 185 (1973), 445–62.
[114] H., Moscovici, Topological Frobenius properties for nilpotent Lie groups. Rev. Roumaine Math. Pures Appl., 19 (1974), 421–5.
[115] O.A., Nielsen, The failure of the topological Frobenius property for nilpotent Lie groups. Math. Scand., 45 (1979), 305–10.
[116] O.A., Nielsen, The failure of the topological Frobenius property for nilpotent Lie groups. II. Math. Ann., 256 (1981), 561–8.
[117] O.A., Nielsen, Unitary Representations and Coadjoint Orbits of Low-dimensional Nilpotent Lie Groups. Queen's Papers in Pure and Applied Mathematics 63. Kingston, Ont., 1983.
[118] M., Nilsen, The Stone–Č. ech compactification of Prim A. Bull. Austral. Math. Soc., 52 (1995), 377–83.
[119] N., Obata, Some remarks on induced representations of infinite discrete groups. Math. Ann., 284 (1989), 91–102.
[120] B., Ørstedt, Induced representations and a newproof of the imprimitivity theorem.J. Funct. Anal., 31 (1979), 355–9.
[121] J., Packer and I., Raeburn, On the structure of twisted group C*-algebras. Trans. Amer. Math. Soc., 334 (1992), 685–718.
[122] G.K., Pedersen, Analysis Now. Graduate Texts in Mathematics 118. New York: Springer-Verlag, 1989.
[123] D., Poguntke, Der Raum der primitiven Ideale von endlichen Erweiterungen lokalkompakter Gruppen. Arch. Math. (Basel), 28 (1977), 133–8.
[124] D., Poguntke, Simple quotients of group C*-algebras for two step nilpotent groups and connected Lie groups. Ann. Éc. Norm. Sup. (4), 16 (1983), 151–72.
[125] L.S., Pontryagin, Topological Groups. Princeton Mathematical Series 2. Princeton, NJ: Princeton University Press, 1939. Translated from the Russian by Emma, Lehmer.
[126] N.S., Poulsen, On C∞-vectors and intertwining bilinear forms for representations of Lie groups. J. Funct. Anal., 9 (1972), 87–120.
[127] J.C., Quigg, On the irreducibility of an induced representation. Pacific J. Math., 93 (1981), 163–79.
[128] J.C., Quigg, On the irreducibility of an induced representation. II. Proc. Amer. Math. Soc., 86 (1982), 345–8.
[129] I., Raeburn, On group C*-algebras of bounded representation dimension. Trans. Amer. Math. Soc., 272 (1982), 629–44.
[130] M.S., Raghunathan, Discrete Subgroups of Lie Groups. New York: Springer, 1972.
[131] A., Ramsay, Non-transitive quasi-orbits in Mackey's analysis of group extensions. Acta Math., 137 (1976), 17–48.
[132] M.A., Rieffel, Unitary representations induced from compact subgroups. Studia Math., 42 (1972), 145–75.
[133] M.A., Rieffel, Induced representations of C*-algebras. Adv. Math., 13 (1974), 176–257.
[134] M.A., Rieffel, Unitary representations of group extensions: an algebraic approach to the theory of Mackey and Blattner. Studies in Analysis, Adv. Math. Suppl. Studies (1969), 43–82.
[135] A., Robert, Introduction to the Representation Theory of Compact and Locally Compact Groups. LMS Lecture Note Series 80. Cambridge: Cambridge University Press, 1983.
[136] D.J.S., Robinson, Finiteness Conditions and Generalized Soluble Groups. I. Berlin: Springer, 1972.
[137] J.M., Rosenberg, The C*-algebras of some real and p-adic solvable groups. Pacific J. Math., 65 (1976), 175–92.
[138] W., Rudin, Fourier Analysis on Groups. Interscience Tracts in Pure and Applied Mathematics 12. New York: Interscience, 1960.
[139] I.E., Schochetman, Topology and the duals of certain locally compact groups. Trans. Amer. Math. Soc., 150 (1970), 477–89.
[140] I.E., Schochetman, Compact and Hilbert–Schmidt induced representations. Duke Math. J., 41 (1974), 89–102.
[141] I.E., Schochetman, The dual topology of certain group extensions. Adv. Math., 35 (1980), 113–28.
[142] E., Schulz and K.F., Taylor, Extensions of the Heisenberg group and wavelet analysis in the plane. In: Spline Functions and the Theory of Wavelets, CRM Proceedings and Lecture Notes 18, eds., D., Serge and D., Gilles (1999), 99–107.
[143] I.E., Segal, Irreducible representations of operator algebras. Bull. Amer. Math. Soc., 53 (1947), 73–88.
[144] G.E., Shilov, On the decomposition of a commutative normed ring into a direct sum of ideals. Mat. Sb., 32 (1954), 353–64.
[145] E.M., Stein, Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals. Princeton, NJ: Princeton University Press, 1993.
[146] E.M., Stein and G., Weiss, Introduction to Fourier Analysis on Euclidean Spaces. Princeton, NJ: Princeton University Press, 1971.
[147] A.I., Stern, The connection between the topologies of a locally bicompact group and its dual space. Funkc. Anal. Pril., 5 (1971), 56–63.
[148] M., Takesaki, Theory of Operator Algebras. I. Berlin: Springer, 1979.
[149] A., Valette, Minimal projections, integrable representations and property (T). Arch. Math. (Basel), 43 (1984), 397–406.
[150] A., Weil, L'intégration dans les Groupes Topologiques et ses Applications. Actualités Sci. et Ind. 869. Paris: Herman et Cie., 1941.
[151] D.P., Williams, The topology on the primitive ideal space of transformation group C*-algebras and CCR transformation group C*-algebras. Trans. Amer. Math. Soc., 266 (1981), 335–59.
[152] D.P., Williams, The structure of crossed products by smooth actions. J. Austral. Math. Soc., 47 (1989), 226–35.
[153] D.P., Williams, Crossed Product C*-algebras. Math. Surveys and Monographs 134. Providence, RI: American Mathematical Society, 2007.
[154] A., Zygmund, Trigonometric Series, II. Cambridge: Cambridge University Press, 1959.