A Review of Prolate Spheroidal Wave Functions from the Perspective of Spectral Methods
DOI:
https://doi.org/10.4208/jms.v50n2.17.01Keywords:
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.