Miscellaneous Properties of PSWFs

  • Andrei Osipov
  • Vladimir Rokhlin
  • Hong Xiao
Chapter
Part of the Applied Mathematical Sciences book series (AMS, volume 187)

Abstract

Prolate spheroidal wave functions possess a rich set of properties. In this chapter, we list some of those properties. Some of the identities below can be found in [13, 33, 64]; others are easily derivable from the former (see also [73]).

Keywords

Prolate 

Bibliography

  1. [13]
    C. Flammer, Spheroidal Wave Functions, Stanford, CA: Stanford University Press, 1956.Google Scholar
  2. [14]
    W. H. J. Fuchs, On the eigenvalues of an integral equation arising in the theory of band-limited signals, J. Math. Anal. Appl. 9 317–330 (1964).MathSciNetCrossRefMATHGoogle Scholar
  3. [33]
    H. J. Landau, H. O. Pollak, Prolate spheroidal wave functions, Fourier analysis, and uncertainty - II, Bell Syst. Tech. J. January 65–94, 1961.Google Scholar
  4. [64]
    D. Slepian, H. O. Pollak, Prolate spheroidal wave functions, Fourier analysis, and uncertainty - I, Bell Syst. Tech. J. January 43–63, 1961.Google Scholar
  5. [67]
    D. Slepian, Some asymptotic expansions for prolate spheroidal wave functions, J. Math. Phys. 44 99–140, 1965.MathSciNetMATHGoogle Scholar
  6. [73]
    H. Xiao, V. Rokhlin, N. Yarvin, Prolate spheroidal wavefunctions, quadrature and interpolation, Inverse Problems, 17(4):805–828, 2001.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

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 CaliforniaDavisUSA

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