# 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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