A Riemann--Lebesgue lemma for Jacobi expansions
Classical Analysis and ODEs
2016-09-06 v1
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.
Cite
@article{arxiv.math/9504215,
title = {A Riemann--Lebesgue lemma for Jacobi expansions},
author = {George Gasper and Walter Trebels},
journal= {arXiv preprint arXiv:math/9504215},
year = {2016}
}