Integral transforms

  • Wilhelm Magnus
  • Fritz Oberhettinger
  • Raj Pal Soni
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 52)


A function g(y) of a variable y (which may be complex) is called the integral transform of a function f(x) with respect to a kernel K(x, y) when
$$g(y) = \int\limits_a^b {K(x,y)f(x)} dx.$$


Inversion Formula Jacobian Elliptic Function Orthogonal Coordinate System Fourier Cosine Fourier Sine 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bochner, S.: Lectures on Fourier integrals. Princeton 1959.Google Scholar
  2. Doetsch, G.: Handbuch der Theorie der Laplace-Transformation. Basel: Birkhauser 1950–1956.Google Scholar
  3. Hirschmann, I. I., and D. V. Widder: The convolution transform. Princeton 1955.Google Scholar
  4. Sneddon, I. N.: Fourier Transforms. New York: MacGraw-Hill 1951.Google Scholar
  5. Titchmarsh, E. C.: Introduction to the theory of Fourier integrals. Oxford 1948.Google Scholar

Literature concerning tables

  1. Erdélyi, A.: Tables of integral transforms. 2 vols. New York: McGraw-Hill 1954.Google Scholar
  2. Oberhettinger, F.: Tabellen zur Fourier-Transformation. Berlin/Göttingen/Heidelberg: Springer 1957.zbMATHCrossRefGoogle Scholar
  3. Oberhettinger, F.: Tables of Laplace and Mellin transforms. Berlin/Heidelberg/New York: Springer (To be published).Google Scholar
  4. Oberhettinger, F., and T. P. Higgins: Tables of Lebedev, Mehler, and generalized Mehler transforms. Report Boeing Scientific Research Laboratories, Seattle, 1961.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1966

Authors and Affiliations

  • Wilhelm Magnus
    • 1
  • Fritz Oberhettinger
    • 2
  • Raj Pal Soni
    • 3
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityUSA
  2. 2.Oregon State UniversityUSA
  3. 3.International Business Machines CorporationUSA

Personalised recommendations