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On generalized functions

Published online by Cambridge University Press:  14 July 2016

B. C. Rennie
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Abstract

There are described in the literature many spaces of what are variously described as generalized functions, distributions, or improper functions. This article introduces another. The new space is like that of M. J. Lighthill in containing the Fourier transform of every element and in having a particularly simple theory of trigonometric and Fourier series; also it is constructed in a somewhat similar way. The new space breaks away from the tradition of every element being, for some n, the nth derivative of an ordinary function, and, for example, the exponential function and its Fourier transform are in the space.

Keywords

DISTRIBUTIONSIMPROPER FUNCTIONSFOURIER SERIESFOURIER TRANSFORMSGENERALIZED FUNCTIONS

Information

Type
Part 3 — Mathematics
Information
Journal of Applied Probability , Volume 19 , Issue A , 1982 , pp. 139 - 156
Copyright
Copyright © 1982 Applied Probability Trust 

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References

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