Spherical associated homogeneous distributions on Rn

dc.contributor.author	Franssens, G.R.
dc.date	2010
dc.date.accessioned	2016-03-30T12:01:17Z
dc.date.available	2016-03-30T12:01:17Z
dc.identifier.uri	https://orfeo.belnet.be/handle/internal/3174
dc.description	A structure theorem for spherically symmetric associated homogeneous distributions (SAHDs) based on Rn is given. It is shown that any SAHD is the pullback, along the function \|x\|λ,\ λ∈C, of an associated homogeneous distribution (AHD) on R. The pullback operator is found not to be injective and its kernel is derived (for λ=1). Special attention is given to the basis SAHDs, Dmz\|x\|z, which become singular when their degree of homogeneity z=−n−2p, ∀p∈N. It is shown that (Dmz\|x\|z)z=−n−2p are partial distributions which can be non-uniquely extended to distributions ((Dmz\|x\|z)e)z=−n−2p and explicit expressions for their evaluation are derived. These results serve to rigorously justify distributional potential theory in Rn.
dc.language	eng
dc.title	Spherical associated homogeneous distributions on Rn
dc.type	Article
dc.subject.frascati	Mathematics
dc.audience	Scientific
dc.source.title	Bulletin of the Belgian Mathematical Society - Simon Stevin
dc.source.volume	17
dc.source.issue	5 SUPPL.
dc.source.page	781-806
Orfeo.peerreviewed	Yes
dc.identifier.scopus	2-s2.0-78651271404