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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Regularity properties of distributions and ultradistributions


Authors: S. Pilipovic and D. Scarpalezos
Journal: Proc. Amer. Math. Soc. 129 (2001), 3531-3537
MSC (2000): Primary 46F05, 46F30, 03C20
Published electronically: June 28, 2001
MathSciNet review: 1860484
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Abstract:

We give necessary and sufficient conditions for a regularized net of a distribution in an open set $\Omega$which imply that it is a smooth function or $C^k$ function in $\Omega$. We also give necessary and sufficient conditions for an ultradistribution to be an ultradifferentiable function of corresponding class.


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Additional Information

S. Pilipovic
Affiliation: Institute of Mathematics, University of Novi Sad, Trg D.Obradovića 4, 21000 Novi Sad, Yugoslavia

D. Scarpalezos
Affiliation: U.F.R. de Mathématiques, Universite Paris 7, 2 place Jussieu, Paris 5$\buildrel e \over{}$, 75005, France

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06013-0
PII: S 0002-9939(01)06013-0
Received by editor(s): February 21, 2000
Published electronically: June 28, 2001
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2001 American Mathematical Society