Almost Everywhere Convergence of Prolate Spheroidal Series
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | JAMING, Philippe | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | SPECKBACHER, Michael | |
| dc.date.accessioned | 2024-04-04T02:57:43Z | |
| dc.date.available | 2024-04-04T02:57:43Z | |
| dc.date.issued | 2020 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192587 | |
| dc.description.abstractEn | 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 $1<p<\infty$, even in the cases when they might not converge in $L^p$-norm. We thereby consider the classical Paley-Wiener spaces $PW_c^p\subset L^p(\R)$ of functions whose Fourier transform is supported in $[-c,c]$ and Paley-Wiener like spaces $B_{\al,c}^p\subset L^p(0,\infty)$ of functions whose Hankel transform $\H^\al$ is supported in $[0,c]$.As a side product, we show the continuity of the projection operator $P_c^\al f:=\H^\al(\chi_{[0,c]}\cdot \H^\al f)$ from $L^p(0,\infty)$ to $L^q(0,\infty)$, $1<p\leq q<\infty$. | |
| dc.language.iso | en | |
| dc.subject.en | Prolate spheroidal wave functions | |
| dc.subject.en | almost everywhere convergence | |
| dc.subject.en | Paley-Wiener type spaces | |
| dc.subject.en | Hankel transform | |
| dc.subject.en | spherical Bessel functions 2010 MSC: 42B10 | |
| dc.subject.en | 42C10 | |
| dc.subject.en | 44A15 | |
| dc.title.en | Almost Everywhere Convergence of Prolate Spheroidal Series | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Analyse classique [math.CA] | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| dc.subject.hal | Mathématiques [math]/Variables complexes [math.CV] | |
| dc.identifier.arxiv | 2001.04287 | |
| bordeaux.journal | Illinois Journal of Mathematics | |
| bordeaux.page | 467-479 | |
| bordeaux.volume | 64 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-02436167 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02436167v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Illinois%20Journal%20of%20Mathematics&rft.date=2020&rft.volume=64&rft.spage=467-479&rft.epage=467-479&rft.au=JAMING,%20Philippe&SPECKBACHER,%20Michael&rft.genre=article |
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