BOULSANE, Mourad; JAMING, Philippe; SOUABNI, Ahmed

doi:10.1016/j.jfa.2019.108295

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BOULSANE, Mourad
University of Carthage

JAMING, Philippe
Institut de Mathématiques de Bordeaux [IMB]

SOUABNI, Ahmed
Université de Carthage (Tunisie) [UCAR]

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Journal of Functional Analysis. 2019, vol. 277, p. 108295

Elsevier

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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 Barceló 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).< Réduire

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mean convergence

prolate spheroidal wave function

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Mean convergence of prolate spheroidal series and their extensions

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