Hermite and Laguerre wave packet expansions
Studia Mathematica (1997)
- Volume: 126, Issue: 3, page 199-217
- ISSN: 0039-3223
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topEpperson, Jay. "Hermite and Laguerre wave packet expansions." Studia Mathematica 126.3 (1997): 199-217. <http://eudml.org/doc/216451>.
@article{Epperson1997,
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.},
author = {Epperson, Jay},
journal = {Studia Mathematica},
keywords = {expansions; Hermite and Laguerre functions; wave packets; Christoffel-Darboux formula for orthogonal polynomials; oscillatory integrals},
language = {eng},
number = {3},
pages = {199-217},
title = {Hermite and Laguerre wave packet expansions},
url = {http://eudml.org/doc/216451},
volume = {126},
year = {1997},
}
TY - JOUR
AU - Epperson, Jay
TI - Hermite and Laguerre wave packet expansions
JO - Studia Mathematica
PY - 1997
VL - 126
IS - 3
SP - 199
EP - 217
AB - 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.
LA - eng
KW - expansions; Hermite and Laguerre functions; wave packets; Christoffel-Darboux formula for orthogonal polynomials; oscillatory integrals
UR - http://eudml.org/doc/216451
ER -
References
top- [1] J. Epperson, Triebel-Lizorkin spaces for Hermite expansions, Studia Math. 114 (1995), 87-103. Zbl0828.42017
- [2] M. Frazier and B. Jawerth, A discrete transform and decompositions of distribution spaces, J. Funct. Anal. 93 (1990), 34-170. Zbl0716.46031
- [3] C. Markett, Mean Cesàro summability of Laguerre expansions and norm estimates with shifted parameter, Anal. Math. 8 (1982), 19-37. Zbl0515.42023
- [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.
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