Almost Everywhere Convergence of Prolate Spheroidal Series

Philippe Jaming (1) , Michael Speckbacher (1)

1 IMB - Institut de Mathématiques de Bordeaux

In this paper, we show that the expansions of functions from $L^p$-Paley-Wiener type spaces in terms of the prolate spheroidal wave functions converge almost everywhere for $1

Mots clés: Prolate spheroidal wave functions; almost everywhere convergence; Paley-Wiener type spaces; Hankel transform; spherical Bessel functions 2010 MSC: 42B10; 42C10; 44A15

Domaines: Analyse classique [math.CA]; Analyse fonctionnelle [math.FA]; Variables complexes [math.CV]

Philippe Jaming, Michael Speckbacher. Almost Everywhere Convergence of Prolate Spheroidal Series. Illinois Journal of Mathematics, 2020, 64, pp.467-479. ⟨hal-02436167⟩