Transform Analysis of Generalized Functions


  • O.P. Misra
  • J.L. Lavoine

Transform Analysis of Generalized Functions concentrates on finite parts of integrals, generalized functions and distributions. It gives a unified treatment of the distributional setting with transform analysis, i.e. Fourier, Laplace, Stieltjes, Mellin, Hankel and Bessel Series.Included are accounts of applications of the theory of integral transforms in a distributional setting to the solution of problems arising in mathematical physics. Information on distributional solutions of differential, partial differential equations and integral equations is conveniently collected here.The volume will serve as introductory and reference material for those interested in analysis, applications, physics and engineering.
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Book information

  • Published: January 1986
  • Imprint: NORTH-HOLLAND
  • ISBN: 978-0-444-87885-4

Table of Contents

Preliminaries. Finite Parts of Integrals. Base Spaces. Definition of Distributions. Properties of Generalized Functions and Distributions. Operations on Generalized Functions and Distributions. Other Operations on Distributions. The Fourier Transformation. The Laplace Transformation. Applications of the Laplace Transformation. The Stieltjes Transformation. The Mellin Transformation. Hankel Transformation and Bessel Series. Bibliography. Author Index.