$L^p$-Convergence of Fourier-Heckman-Opdam Expansions

Béchir Amri

doi:10.48550/arxiv.2601.08582

$L^p$-Convergence of Fourier-Heckman-Opdam Expansions

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Béchir Amri

DOI: 10.48550/arxiv.2601.08582

Cited by: 0

Abstract

We study the $L^p$-convergence of Fourier expansions in terms of non-symmetric Heckman-Opdam polynomials of type $A_1$. Using kernel estimates and duality arguments, we prove that the partial sums converge in $ L^p([-π,π],dm_k)$ for $$2-\frac{1}{k+1} < p < 2+\frac{1}{k}.$$

Fields of Study & Subjects

Mathematical functions and polynomials Mathematical Analysis and Transform Methods Approximation Theory and Sequence Spaces

Publication details

Journal / source: arXiv (Cornell University)
Publication date: 13 January 2026
Document type: Preprint