A Review of Prolate Spheroidal Wave Functions from the Perspective of Spectral Methods

Authors

  • Li-Lian Wang

DOI:

https://doi.org/10.4208/jms.v50n2.17.01

Keywords:

Prolate spheroidal wave functions and their generalisations, time-frequency concentration problem, bandlimited functions, finite Fourier ⁄ Hankel transforms, quasi-uniform grids, well-conditioned prolate collocation scheme, prolate-Galerkin method, spectral accuracy.

Abstract

This paper is devoted to a review of the prolate spheroidal wave functions (PSWFs) and their variants from the viewpoint of spectral ⁄ spectral-element approximations using such functions as basis functions. We demonstrate the pros and cons over their polynomial counterparts, and put the emphasis on the construction of essential building blocks for efficient spectral algorithms.

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Published

2017-06-02

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Issue

Vol. 50 No. 2 (2017)

Section

Articles

How to Cite

A Review of Prolate Spheroidal Wave Functions from the Perspective of Spectral Methods. (2017). Journal of Mathematical Study, 50(2), 101-143. https://doi.org/10.4208/jms.v50n2.17.01