TY - JOUR
T1 - A Review of Prolate Spheroidal Wave Functions from the Perspective of Spectral Methods
AU - Wang , Li-Lian
JO - Journal of Mathematical Study
VL - 2
SP - 101
EP - 143
PY - 2017
DA - 2017/06
SN - 50
DO - http://doi.org/10.4208/jms.v50n2.17.01
UR - https://global-sci.org/intro/article_detail/jms/10005.html
KW - 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.
AB - <p style="text-align: justify;">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.</p>