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Generalized functions for applications

Published online by Cambridge University Press:  17 February 2009

B. D. Craven
Affiliation:
Mathematics Department, University of Melbourne, Parkville, Victoria 3052 and Visiting Scientist at the National Research Institute for Mathematical Sciences of the CSIR, Pretoria, South Africa.
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Abstract

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A simple rigorous approach is given to generalized functions, suitable for applications. Here, a generalized function is defined as a genuine function on a superset of the real line, so that multiplication is unrestricted and associative, and various manipulations retain their classical meanings. The superset is simply constructed, and does not require Robinson's nonstandard real line. The generalized functions go beyond the Schwartz distributions, enabling products and square roots of delta functions to be discussed.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1985

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