Prolate Spheroidal Wave Functions of Order Zero, 1st Edition

  • Published By:
  • ISBN-10: 1461482593
  • ISBN-13: 9781461482598
  • DDC: 530.12
  • Grade Level Range: College Freshman - College Senior
  • 379 Pages | eBook
  • Original Copyright 2013 | Published/Released June 2014
  • This publication's content originally published in print form: 2013

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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.

Table of Contents

Front Cover.
Other Frontmatter.
Title Page.
Copyright Page.
1: Introduction.
2: Mathematical and Numerical Preliminaries.
3: Overview.
4: Analysis of a Differential Operator.
5: Analysis of the Integral Operator.
6: Rational Approximations of PSWFs.
7: Miscellaneous Properties of PSWFs.
8: Asymptotic Analysis of PSWFs.
9: Quadrature Rules and Interpolation via PSWFs.
10: Numerical Algorithms.