Pré-Publication, Document De Travail Année : 2023

Random zonal eigenfunctions and a Hölder version of the Paley-Zygmund theorem on compact manifolds

Résumé

We study the convergence of Gaussian random series of radial/zonal eigenfunctions of the Laplace-Beltrami operator (on the Euclidean space and on the round sphere). More precisely, we obtain a simple necessary and sufficient condition of almost sure uniform convergence (we thus complete an analysis of Ayache and Tzvetkov). In dimension two, our strategy turns out to be linked with Hölder regularities. As a by-product, we also prove a Hölder version of the Paley-Zygmund theorem on a boundaryless Riemannian compact manifold.

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Dates et versions

hal-05091946 , version 1 (01-06-2025)

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  • HAL Id : hal-05091946 , version 1

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Pierre Brun, Rafik Imekraz, Guillaume Poly. Random zonal eigenfunctions and a Hölder version of the Paley-Zygmund theorem on compact manifolds. 2023. ⟨hal-05091946⟩
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