Convolution product formula for associated homogeneous distributions on R

dc.contributor.author	Franssens, G.R.
dc.date	2011
dc.date.accessioned	2016-03-29T12:43:51Z
dc.date.available	2016-03-29T12:43:51Z
dc.identifier.uri	https://orfeo.belnet.be/handle/internal/3076
dc.description	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.
dc.language	eng
dc.title	Convolution product formula for associated homogeneous distributions on R
dc.type	Article
dc.subject.frascati	Mathematics
dc.audience	Scientific
dc.subject.free	Convolution structure
dc.subject.free	Functional extension
dc.subject.free	Generalized functions
dc.subject.free	Homogeneous distribution
dc.subject.free	real line
dc.subject.free	Convolution
dc.source.title	Mathematical Methods in the Applied Sciences
dc.source.volume	34
dc.source.issue	6
dc.source.page	703-727
Orfeo.peerreviewed	Yes
dc.identifier.doi	10.1002/mma.1397
dc.identifier.scopus	2-s2.0-79953283752