A Riemann--Lebesgue lemma for Jacobi expansions

1995/04/12 by Gasper, George, Trebels, Walter
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/9504215

Abstract

A Lemma of Riemann--Lebesgue type for Fourier--Jacobi coefficients is derived. Via integral representations of Dirichlet--Mehler type for Jacobi polynomials its proof directly reduces to the classical Riemann--Lebesgue Lemma for Fourier coefficients. Other proofs are sketched. Analogous results are also derived for Laguerre expansions and for Jacobi transforms.

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