Download PDF - Hermite and Laguerre wave packet expansionsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Hermite and Laguerre wave packet expansions

Authors 1

Affiliations

  1. Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131, U.S.A.

Abstract

This paper describes expansions in terms of Hermite and Laguerre functions similar to the Frazier-Jawerth expansion in Fourier analysis. The wave packets occurring in these expansions are finite linear combinations of Hermite and Laguerre functions. The Shannon sampling formula played an important role in the derivation of the Frazier-Jawerth expansion. In this paper we use the Christoffel-Darboux formula for orthogonal polynomials instead. We obtain estimates on the decay of the Hermite and Laguerre wave packets by investigating two closely related oscillatory integrals.

Bibliography

  1. J. Epperson, Triebel-Lizorkin spaces for Hermite expansions, Studia Math. 114 (1995), 87-103.
  2. M. Frazier and B. Jawerth, A discrete transform and decompositions of distribution spaces, J. Funct. Anal. 93 (1990), 34-170.
  3. C. Markett, Mean Cesàro summability of Laguerre expansions and norm estimates with shifted parameter, Anal. Math. 8 (1982), 19-37.
  4. E. Rainville, Special Functions, Macmillan, New York, 1960.
  5. G. Szegő, Orthogonal Polynomials, Amer. Math. Soc. Colloq. Publ. 23, Providence, R.I., 1975.
  6. S. Thangavelu, Lectures on Hermite and Laguerre Expansions, Math. Notes 42, Princeton Univ. Press, 1993.
Studia Mathematica
1997/126/3
Export to PBN, Opens in new tab
Pages:
199-217
Main language of publication
English
Received
1995-10-09
Accepted
1996-12-09
Published
1997
Exact and natural sciences