English

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.

Keywords

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}
}
R2 v1 2026-07-22T17:55:30.370Z