Transforms in Several Variables

  • Brian Davies
Part of the Texts in Applied Mathematics book series (TAM, volume 41)


In this short chapter, we sketch a little of the theory of Fourier transforms in several variables. There are other combinations that may occur in applications, for example, mixed transforms such as a Laplace transform in combination with a Fourier transform. Since they are usually required on a case-by-case basis, we do not attempt to a general treatment here.1


Fourier Transform Radiation Condition Order Partial Differential Equation Fresnel Diffraction Fraunhofer Diffraction 
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  1. 10.
    J.C. Jaeger, Bull. Am. Math. Soc., 46 (1940), 687.MathSciNetCrossRefGoogle Scholar
  2. 11.
    The application of the double Laplace transform to a more general second- order partial differential equation in the quadrant x ≥ 0, y ≥ 0 is discussed in K. Evans and E.A. Jackson, J. Math. Phys., 12 (1971), 2012.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 2002

Authors and Affiliations

  • Brian Davies
    • 1
  1. 1.Mathematics Department, School of Mathematical SciencesAustralian National UniversityCanberraAustralia

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