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Convolution product formula for associated homogeneous distributions on R

✍ Scribed by Ghislain R. Franssens

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
343 KB
Volume
34
Category
Article
ISSN
0170-4214

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✦ Synopsis

The set of Associated Homogeneous Distributions (AHDs) on R, H (R), consists of distributional analogues of power-log functions with domain in R. This set contains the majority of the (one-dimensional) distributions typically encountered in physics applications.

In earlier work of the author it was shown that H (R) admits a closed convolution structure, provided that critical convolution products are defined by a functional extension process. In this paper, the general convolution product formula is derived. Convolution of AHDs on R is found to be associative, except for critical triple products. Critical products are shown to be non-associative in a minimal and interesting way.

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## Abstract Associated homogeneous distributions (AHDs) with support in the line **R** are the distributional generalizations of one‐dimensional power‐log functions. In this paper, we derive a number of practical structure theorems for AHDs based on **R** and being complex analytic with respect to