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<p>In this paper, we give various explicit and local estimates of ball prolate spheroidal wave functions (ball PSWFs) that have been defined in [<CitationRef CitationID="CR1">1</CitationRef>] as common eigenfunctions of the finite Fourier transform and a differential operator. In particular, we give further refined bounds of these functions and their associated eigenvalues. As a consequence, we show that ball PSWFs are well adapted for the approximation of almost band-limited functions. Moreover, we compare this approximation result with the one obtained in the classical framework of ball polynomials.</p>

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Further Properties of Ball Prolates and Approximation of Related Almost Band-Limited Functions

  • 期刊论文

  • 发表日期：

    2025年7月4日

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  • Ahmed Souabni

摘要

In this paper, we give various explicit and local estimates of ball prolate spheroidal wave functions (ball PSWFs) that have been defined in [1] as common eigenfunctions of the finite Fourier transform and a differential operator. In particular, we give further refined bounds of these functions and their associated eigenvalues. As a consequence, we show that ball PSWFs are well adapted for the approximation of almost band-limited functions. Moreover, we compare this approximation result with the one obtained in the classical framework of ball polynomials.