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Introduction

In: Fundamental Solutions for Differential Operators and Applications

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  • Prem K. Kythe

    (University of New Orleans, Department of Mathematics)

Abstract

The theory of distributions has proved to be essential in the study of partial differential equations. In 1975, F. E. Browder stated: ‘In considering the applications of functional analysis in partial differential equations and in Fourier series analysis the theory of distributions stands out as an important and curious turning point’. The prerequisites for the development of the theory of distributions, namely, the Heaviside’s operational calculus, generalized derivatives and generalized solutions of differential equations, generalized Fourier transforms, Dirac’s delta function and other improper functions, and de Rham’s currents, were already available prior to 1950 when the first monograph on the theory of distributions was published by L. Schwartz. Since then the mathematicians and physicists started to use distributions (generalized functions) in their investigation of problems of applied mathematics and theoretical physics.

Suggested Citation

  • Prem K. Kythe, 1996. "Introduction," Springer Books, in: Fundamental Solutions for Differential Operators and Applications, pages 1-10, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-4106-5_1
    DOI: 10.1007/978-1-4612-4106-5_1
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