Generalized Functions

  • D. G. Crighton
  • A. P. Dowling
  • J. E. Ffowcs Williams
  • M. Heckl
  • F. G. Leppington

Abstract

It is an object of this Chapter to remove some of the mystique associated with generalized functions and to advocate their use in the analysis of physical problems. We will define their properties without proof and direct those interested in pursuing the fundamentals of generalized functions to Lighthill (1958), Gelfand & Shilov (1964) and Jones (1966) who give comprehensive accounts of the general theory with proofs of properties. We lean heavily on these works in recognizing that generalized functions can essentially be manipulated according to the usual rules of addition, differentiation and integration, though in general they may not be multiplied by other than ordinary functions. They provide a powerful extension of the normal mathematical equipment available to physicists.

Keywords

Convolution Acoustics 

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Referencess

  1. Lighthill, M.J. (1958) Fourier Analysis and Generalised Functions. Cambridge University Press.Google Scholar
  2. Gelfand, I.M. & Shilov, G.E. (1964) Generalised Functions. Academic Press.Google Scholar
  3. Jones, D.S. (1966) Generalised Functions. McGraw-Hill.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • D. G. Crighton
    • 1
  • A. P. Dowling
    • 2
  • J. E. Ffowcs Williams
    • 2
  • M. Heckl
    • 3
  • F. G. Leppington
    • 4
  1. 1.University of CambridgeUK
  2. 2.Department of EngineeringUniversity of CambridgeUK
  3. 3.Technische Universität BerlinGermany
  4. 4.The Imperial College of Science and TechnologyLondonUK

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