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Mathematics - Computational Science & Engineering | Prolate Spheroidal Wave Functions of Order Zero - Mathematical Tools for Bandlimited Approximation

Prolate Spheroidal Wave Functions of Order Zero

Mathematical Tools for Bandlimited Approximation

Series: Applied Mathematical Sciences, Vol. 187

Osipov, Andrei, Rokhlin, Vladimir, Xiao, Hong

2013, XI, 379 p. 30 illus.

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  • Aimed at a broad spectrum of scientists and engineers
  • Contains detailed description of practical numerical algorithms
  • Written by top international researchers in field

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 PSWF as an analytical tool to electrical engineers designing filters and antennas.

Content Level » Research

Keywords » Analytical Tools - Approximate Formulae for PSWF - Evaluation of the Quadrature Nodes - Intuition Behind Quadrature Weights - Numerical Algorithms - Prolate Spheroidal Wave Functions

Related subjects » Computational Intelligence and Complexity - Computational Science & Engineering - Signals & Communication

Table of contents 

​Introduction.- Mathematical and Numerical Preliminaries.- Overview.- Analysis of the 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​.- 

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