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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

Integral Operator Orthonormal Basis Analytic Continuation Recurrence Relation Complex Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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