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dc.contributor.authorFranssens, G.R.
dc.date2010
dc.date.accessioned2016-03-30T12:01:17Z
dc.date.available2016-03-30T12:01:17Z
dc.identifier.urihttps://orfeo.belnet.be/handle/internal/3174
dc.descriptionA 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.languageeng
dc.titleSpherical associated homogeneous distributions on Rn
dc.typeArticle
dc.subject.frascatiMathematics
dc.audienceScientific
dc.source.titleBulletin of the Belgian Mathematical Society - Simon Stevin
dc.source.volume17
dc.source.issue5 SUPPL.
dc.source.page781-806
Orfeo.peerreviewedYes
dc.identifier.scopus2-s2.0-78651271404


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