Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-10T19:58:38.434Z Has data issue: false hasContentIssue false
  • English
  • Français

On Necessary Multiplier Conditions for Laguerre Expansions

Published online by Cambridge University Press:  20 November 2018

George Gasper  and
Walter Trebels
George Gasper
Affiliation:
Department of Mathematics, Northwestern University, Evanston, IL 60208, U.S.A.
Walter Trebels
Affiliation:
Technische Hochschule, Darmstadt, Germany
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Necessary multiplier conditions for Laguerre expansions are derived and discussed within the framework of weighted Lebesgue spaces.

Keywords

33A6542A4542C10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 6 , 01 December 1991 , pp. 1228 - 1242
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Askey, R., Dual equations and classical orthogonal polynomials, J. Math. Anal. Appl. 24(1968), 677–685.Google Scholar
2. Askey, R. and Wainger, S., Mean convergence of expansions in Laguerre andHermite series, Amer. J. Math. 87(1965), 695–708.Google Scholar
3. Dhigosz, J., LP -multipliers for the Laguerre expansions, Colloq. Math. 54(1987), 285–293.Google Scholar
4. Erdelyi, A. et al., Higher transcendental functions, vols. I & II. McGraw Hill, New York, 1953.Google Scholar
5. Gasper, G. and Trebels, W., A characterization of localized Bessel potential spaces and applications to Jacobi andHankel multipliers, Studia Math. 65(1979), 243–278.Google Scholar
6. Gasper, G. and Trebels, W., A Hausdorff-Young inequality and necessary multiplier conditions for Jacobi expansions, Acta Sci. Math. 42(1980), 247–255.Google Scholar
7. Gasper, G. and Trebels, W., Necessary conditions for Hankel multipliers, Indiana Univ. Math. J. 31(1982), 403–414.Google Scholar
8. Görlich, E. and Markett, C., Estimates for the norm of the Laguerre translation operator, Numer. Funct. Anal. Optim. 1(1979), 203–222.Google Scholar
9. Görlich, E. and Markett, C., A convolution structure for Laguerre series, Indag. Math. 44(1982), 161–171.Google Scholar
10. Kanjin, Y., A transplantation theorem for Laguerre series, to appear.Google Scholar
11. Luke, Y.L., The special functions and their approximations, vols. I & II. Academic Press, New York, 1969.Google Scholar
12. Markett, C., Norm estimates for Cesàro means of Laguerre expansions, in Approximation and Function Spaces (Gdansk 1979), pp. 419–435. North Holland, Amsterdam, 1981.Google Scholar
13. Markett, C., Nikolskii-Type inequalities for Laguerre andHermite expansions, Coll. Math. Soc. János Bolyai, Budapest 35(1980), pp. 811–834.Google Scholar
14. Markett, C., Mean Cesàro summability of Laguerre expansions and norm estimates with shifted parameter, Anal. Math. 8(1982), 19–37.Google Scholar
15. Muckenhoupt, B., Poisson integrals for Hermite and Laguerre expansions, Trans. Amer. Math. Soc. 139(1969), 231–242.Google Scholar
16. Muckenhoupt, B., Mean convergence of Hermite and Laguerre series II, Trans. Amer. Math. Soc. 147(1970), 433–460.Google Scholar
17. Poiani, E.L., Mean Cesàro summability of Laguerre and Hermite series, Trans. Amer. Math. Soc. 173(1972), 1–31.Google Scholar
18. Stein, E.M. and Weiss, G., Interpolation of operators with change of measures, Trans. Amer. Math. Soc. 87(1958), 159–172.Google Scholar
19. Szegö, G., Orthogonal polynomials. 4th éd., Amer. Math. Soc. Colloq. Publ. 23, Providence, R.I. 1975.Google Scholar
20. Trebels, W., Multipliers for (C, a)-bounded Fourier expansions in Banach spaces and approximation theory. Springer Lecture Notes in Math. 329, Springer-Verlag, Berlin 1973.Google Scholar
21. Tricomi, F.G., Vorlesungen über Orthogonalreihen. Springer-Verlag, 1970.Google Scholar
22. Zeller, K. und Beekmann, W., Theorie der Limitierungsverfahren. 2nd éd., Ergebnisse der Mathematik und ihrer Grenzgebiete, Bd. 15, Springer-Verlag, Berlin 1970.Google Scholar