The convolution of associated homogeneous distributions on R-Part II

Author: Franssens Ghislain  

Publisher: Taylor & Francis Ltd

ISSN: 0003-6811

Source: Applicable Analysis, Vol.88, Iss.3, 2009-03, pp. : 333-356

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Abstract

This is the second in a series of two papers in which we construct a convolution product for the set H' (R) of associated homogeneous distributions (AHDs) with support in R. In Part I we showed that if f a and gb are AHDs with degrees of homogeneity a - 1 and b - 1, the convolution fa * gb exists as an AHD, if the resulting degree of homogeneity a + b-1 ∉ N. In this article, we develop a functional extension process, based on the Hahn-Banach theorem, to give a meaning to the convolution product of two AHDs of degrees a - 1 and b - 1, in the critical case that a + b - 1 ∈ N. With respect to this construction, the structure (H'(R), *) is shown to be closed.