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Prolate Spheroidal Wave Functions of Order Zero

Mathematical Tools for Bandlimited Approximation

  • Andrei Osipov
  • Vladimir Rokhlin
  • Hong Xiao

Part of the Applied Mathematical Sciences book series (AMS, volume 187)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Andrei Osipov, Vladimir Rokhlin, Hong Xiao
    Pages 1-3
  3. Andrei Osipov, Vladimir Rokhlin, Hong Xiao
    Pages 5-32
  4. Andrei Osipov, Vladimir Rokhlin, Hong Xiao
    Pages 33-71
  5. Andrei Osipov, Vladimir Rokhlin, Hong Xiao
    Pages 73-133
  6. Andrei Osipov, Vladimir Rokhlin, Hong Xiao
    Pages 135-169
  7. Andrei Osipov, Vladimir Rokhlin, Hong Xiao
    Pages 171-223
  8. Andrei Osipov, Vladimir Rokhlin, Hong Xiao
    Pages 225-242
  9. Andrei Osipov, Vladimir Rokhlin, Hong Xiao
    Pages 243-274
  10. Andrei Osipov, Vladimir Rokhlin, Hong Xiao
    Pages 275-351
  11. Andrei Osipov, Vladimir Rokhlin, Hong Xiao
    Pages 353-370
  12. Back Matter
    Pages 371-379

About this book

Introduction

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.

Keywords

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

Authors and affiliations

  • Andrei Osipov
    • 1
  • Vladimir Rokhlin
    • 2
  • Hong Xiao
    • 3
  1. 1.Department of MathematicsYale UniversityNew HavenUSA
  2. 2.Department of Computer ScienceYale UniversityNew HavenUSA
  3. 3.Department of Computer ScienceUniversity of California, DavisDavisUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-8259-8
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Springer, Boston, MA
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-8258-1
  • Online ISBN 978-1-4614-8259-8
  • Series Print ISSN 0066-5452
  • Series Online ISSN 2196-968X
  • Buy this book on publisher's site
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