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arXiv · 2601.08582

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

Bechir Amri
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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([-\pi,\pi],dm_k)$ for $$2-\frac{1}{k+1} < p < 2+\frac{1}{k}.$$

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Bechir Amri. 2026-01-13. $L^p$-Convergence of Fourier-Heckman-Opdam Expansions. https://arxiv.org/abs/2601.08582

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