Hermite and Laguerre wave packet expansions

• Autorzy: Jay Epperson
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42C15: General harmonic expansions, frames

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 126
• Numer: 3
• Strony: 199-217

Daty

wydano

1997

otrzymano

1995-10-09

poprawiono

1996-12-09

Twórcy

autor

Jay Epperson

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

Bibliografia

• [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.