Journal Article10.1017/S0308210500017467
Generalised functions and their convolution
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TL;DR: In this paper, a new method of defining the convolution and multiplication of generalised functions, too singular to be encompassed by earlier theories, is developed and its extension to the case of several variables is described.
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Abstract: Some attributes of a new method of defining the convolution and multiplication of generalised functions, too singular to be encompassed by earlier theories, are developed and its extension to the case of several variables is described.
read more
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Citations
Hadamard's Finite Part
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On the square of x-n
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Cardinal interpolation by Dm-splines
T. N. T. Goodman,S. L. Lee +1 more
TL;DR: In this paper, it was shown that higher order cardinal splines can be written as convolutions of lower order ones, using a new notion of convolution due to Jones (1982).
5
References
Infinite Integrals and Convolution
TL;DR: In this paper, a new definition of an infinite integral is discussed, by means of which a convolution can be defined for generalized functions the behaviour of which at infinity is so singular as to prevent them coming within the scope of customary theories but yet are needed in applications.
14
•Book
The theory of generalised functions
D. S. Jones
- 01 Jan 1982
TL;DR: In this article, Jones discusses generalised functions and their applications and provides the simplest introduction for those who wish to learn to use generalized functions and there is liberal provision of exercises with which to gain experience.