Introduction

Prem K. Kythe
Additional contact information
Prem K. Kythe: University of New Orleans, Department of Mathematics

A chapter in Fundamental Solutions for Differential Operators and Applications, 1996, pp 1-10 from Springer

Abstract: 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.

Keywords: Fundamental Solution; Boundary Element Method; Elementary Solution; Hyperbolic Equation; Boundary Integral Equation Method (search for similar items in EconPapers)
Date: 1996
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-4106-5_1

Ordering information: This item can be ordered from
http://www.springer.com/9781461241065

DOI: 10.1007/978-1-4612-4106-5_1

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().