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A new definition of an infinite integral is discussed. By means of it, 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. A Fourier transform gives products such as 8(p)(α). 8(α) 0 as well as providing multiplication rules for many important generalized functions.
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D. S. Jones (1980) studied this question.
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