ON THE IMPOSSIBILITY OF THE CONVOLUTION OF DISTRIBUTIONS

ON THE IMPOSSIBILITY OF THE CONVOLUTION OF DISTRIBUTIONS

Certain incompatibilities are proved related to the prolongation of an associative derivation convolution algebra, defined for a subset of distributions, to a larger subset of distributions containing a derivation and the one distribution. This result is a twin of Schwartz’ impossibility t...

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Autor principal: Franssens,Ghislain R
Lenguaje:English
Publicado: Universidad de La Frontera. Departamento de Matemática y Estadística. 2013
Materias:
Generalized function
Distribution
Convolution algebra
Impossibility theorem
Acceso en línea:http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462013000200007
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spelling oai:scielo:S0719-064620130002000072018-10-08ON THE IMPOSSIBILITY OF THE CONVOLUTION OF DISTRIBUTIONSFranssens,Ghislain R Generalized function Distribution Convolution algebra Impossibility theorem Certain incompatibilities are proved related to the prolongation of an associative derivation convolution algebra, defined for a subset of distributions, to a larger subset of distributions containing a derivation and the one distribution. This result is a twin of Schwartz’ impossibility theorem, stating certain incompatibilities related to the prolongation of the multiplication product from the set of continuous functions to a larger subset of distributions containing a derivation and the delta distribution. The presented result shows that the non-associativity of a recently constructed derivation convolution algebra of associated homogeneous distributions with support in R cannot be avoided.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.15 n.2 20132013-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462013000200007en10.4067/S0719-06462013000200007
institution Scielo Chile
collection Scielo Chile
language English
topic Generalized function
Distribution
Convolution algebra
Impossibility theorem
spellingShingle Generalized function
Distribution
Convolution algebra
Impossibility theorem
Franssens,Ghislain R
ON THE IMPOSSIBILITY OF THE CONVOLUTION OF DISTRIBUTIONS
description Certain incompatibilities are proved related to the prolongation of an associative derivation convolution algebra, defined for a subset of distributions, to a larger subset of distributions containing a derivation and the one distribution. This result is a twin of Schwartz’ impossibility theorem, stating certain incompatibilities related to the prolongation of the multiplication product from the set of continuous functions to a larger subset of distributions containing a derivation and the delta distribution. The presented result shows that the non-associativity of a recently constructed derivation convolution algebra of associated homogeneous distributions with support in R cannot be avoided.
author Franssens,Ghislain R
author_facet Franssens,Ghislain R
author_sort Franssens,Ghislain R
title ON THE IMPOSSIBILITY OF THE CONVOLUTION OF DISTRIBUTIONS
title_short ON THE IMPOSSIBILITY OF THE CONVOLUTION OF DISTRIBUTIONS
title_full ON THE IMPOSSIBILITY OF THE CONVOLUTION OF DISTRIBUTIONS
title_fullStr ON THE IMPOSSIBILITY OF THE CONVOLUTION OF DISTRIBUTIONS
title_full_unstemmed ON THE IMPOSSIBILITY OF THE CONVOLUTION OF DISTRIBUTIONS
title_sort on the impossibility of the convolution of distributions
publisher Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate 2013
url http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462013000200007
work_keys_str_mv AT franssensghislainr ontheimpossibilityoftheconvolutionofdistributions
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