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December 2020 Almost everywhere convergence of prolate spheroidal series
Philippe Jaming, Michael Speckbacher
Illinois J. Math. 64(4): 467-479 (December 2020). DOI: 10.1215/00192082-8622664

Abstract

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 < , even in the cases when they might not converge in L p -norm. We thereby consider the classical Paley–Wiener spaces P W c p L p ( R ) of functions whose Fourier transform is supported in [ c , c ] and Paley–Wiener-like spaces B α , c p L p ( 0 , ) of functions whose Hankel transform H α is supported in [ 0 , c ] . As a side product, we show the continuity of the projection operator P c α f : = H α ( χ [ 0 , c ] H α f ) from L p ( 0 , ) to L q ( 0 , ) , 1 < p q < .

Citation

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Philippe Jaming. Michael Speckbacher. "Almost everywhere convergence of prolate spheroidal series." Illinois J. Math. 64 (4) 467 - 479, December 2020. https://doi.org/10.1215/00192082-8622664

Information

Received: 10 January 2020; Revised: 23 April 2020; Published: December 2020
First available in Project Euclid: 1 July 2020

zbMATH: 07269216
MathSciNet: MR4164442
Digital Object Identifier: 10.1215/00192082-8622664

Subjects:
Primary: 42B10
Secondary: 42C10, 44A15

Rights: Copyright © 2020 University of Illinois at Urbana-Champaign

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Vol.64 • No. 4 • December 2020
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