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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.