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A Riemann--Lebesgue lemma for Jacobi expansions

George Gasper Jr·Walter Trebels
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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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George Gasper Jr, Walter Trebels. 1995-04-12. A Riemann--Lebesgue lemma for Jacobi expansions. https://arxiv.org/abs/math/9504215

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