Osipov A., Rokhlin V., Xiao H. Prolate Spheroidal Wave Functions of Order Zero. Mathematical Tools for Bandlimited Approximation

Springer US 2013. — (Applied Mathematical Sciences 187). — 379 pp. — ISBN: 978-1-4614-8258-1 (Print) 978-1-4614-8259-8 (Online).Prolate Spheroidal Wave Functions (PSWFs) are the eigenfunctions of the bandlimited operator in one dimension. As such, they play an important role in signal processing, Fourier analysis, and approximation theory. While historically the numerical evaluation of PSWFs presented serious difficulties, the developments of the last fifteen years or so made them as computationally tractable as any other class of special functions. As a result, PSWFs have been becoming a popular computational tool.
The present book serves as a complete, self-contained resource for both theory and computation. It will be of interest to a wide range of scientists and engineers, from mathematicians interested in PSWFs as an analytical tool to electrical engineers designing filters and antennas.Aimed at a broad spectrum of scientists and engineers
Contains detailed description of practical numerical algorithms
Written by top international researchers in fieldMathematical and Numerical Preliminaries
Overview
Analysis of a Differential Operator
Analysis of the Integral Operator
Rational Approximations of PSWFs
Miscellaneous Properties of PSWFs
Asymptotic Analysis of PSWFs
Quadrature Rules and Interpolation via PSWFs
Numerical Algorithms.