The convolution of associated homogeneous distributions on R-Part I
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Authors
Franssens, G.R.
Discipline
Mathematics
Audience
Scientific
Date
2009Metadata
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This is the first in a series of two papers in which we construct a convolution product for associated homogeneous distributions (AHDs) with support in R. In this article, we show that if fa and gb are AHDs with degrees of homogeneity a - 1 and b - 1, the convolution fa * gb exists as an AHD, provided the resulting degree of homogeneity a + b - 1 is not a natural number. Under this restriction, it is found that the convolution product of AHDs is bilinear, bicontinuous and associative. New convolution products are derived for several basis AHDs such as half-line distributions, associated Riesz distributions and associated generalizations of Heisenberg distributions.
Citation
Franssens, G.R. (2009). The convolution of associated homogeneous distributions on R-Part I. , Applicable Analysis, Vol. 88, Issue 3, 309-331, DOI: 10.1080/00036810902766674.Identifiers
scopus: 2-s2.0-67651210819
Type
Article
Peer-Review
Yes
Language
eng