A Review of Prolate Spheroidal Wave Functions from the Perspective of Spectral Methods (Journal of Mathematical Study, 2017)
This paper is devoted to a review of the prolate spheroidal wave functions(PSWFs) and their variants from the viewpoint of spectral ⁄ spectral-element approximationsusing such functions as basis functions. We demonstrate the pros and consover their polynomial counterparts, and put the emphasis on the construction of essentialbuilding blocks for efficient spectral algorithms.
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.