Mean convergence of prolate spheroidal series and their extensions
Classical Analysis and ODEs
2018-04-05 v2 Complex Variables
Functional Analysis
Abstract
The aim of this paper is to establish the range of p's for which the expansion of a function f L p in a generalized prolate spheroidal wave function (PSWFs) basis converges to f in L p. Two generalizations of PSWFs are considered here, the circular PSWFs introduced by D. Slepian and the weighted PSWFs introduced by Wang and Zhang. Both cases cover the classical PSWFs for which the corresponding results has been previously established by Barcel{\'o} and Cordoba. To establish those results, we prove a general result that allows to extend mean convergence in a given basis (e.g. Jacobi polynomials or Bessel basis) to mean convergence in a second basis (here the generalized PSWFs).
Keywords
Cite
@article{arxiv.1804.00851,
title = {Mean convergence of prolate spheroidal series and their extensions},
author = {Mourad Boulsane and Philippe Jaming and Ahmed Souabni},
journal= {arXiv preprint arXiv:1804.00851},
year = {2018}
}