Further properties of ball prolates and approximation of related almost band-limited functions

TL;DR

This paper provides refined bounds for ball prolate spheroidal wave functions, demonstrating their effectiveness in approximating almost band-limited functions and comparing their performance with ball polynomials.

Contribution

It offers explicit estimates and bounds for ball PSWFs and their eigenvalues, enhancing understanding of their approximation capabilities for band-limited functions.

Findings

Refined bounds for ball PSWFs and eigenvalues

Ball PSWFs are effective for approximating almost band-limited functions

Comparison shows advantages over ball polynomials

Abstract

In this paper we aim to give various explicit and local estimates of ball prolate spheroidal wave functions defined in [25] as eigenfunctions of both finite Fourier transform and some differential operator. In particular, we give further refined bounds of these functions and their related eigenvalues. As consequence, we show that ball PSWFs are well adapted for the approximation of almost band-limited functions and we compare this result with the one related to the ball polynomials.