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Colombeau generalized ultradistributions

Published online by Cambridge University Press:  18 May 2001

S. PILIPOVIĆ  and
D. SCARPALEZOS
S. PILIPOVIĆ
Affiliation:
Institute of Mathematics, University of Novi Sad, Trg D. Obrado-vića 4, 21000 Novi Sad, Yugoslavia. e-mail: pilipovic@unsim.ns.ac.yu
D. SCARPALEZOS
Affiliation:
U.F.R. de Mathématiques, Université Paris 7, 2 place Jussieu, Paris 5e, 75005, France. e-mail: scarpa@math.jussieu.fr
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Abstract

An algebra of Colombeau generalized ultradistributions in which the corresponding space of ultradistributions is embedded via regularizations and in which the multiplication of ultradifferentiable functions of an appropriate class is the ordinary multiplication is constructed. This enables the development of the local and micro-local analysis in the framework of a new scale of Colombeau algebras. Sufficient conditions for a generalized ultradistribution being an ultradifferentiable function are given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 130 , Issue 3 , May 2001 , pp. 541 - 553
Copyright
2001 Cambridge Philosophical Society

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