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OPTIMAL EMBEDDINGS OF DISTRIBUTIONS INTO ALGEBRAS

Published online by Cambridge University Press:  04 July 2003

H. Vernaeve
H. Vernaeve
Affiliation:
Department of Pure Mathematics and Computer Algebra, University of Ghent, Galglaan 2, B-9000 Gent, Belgium ([email protected])
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Abstract

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Let $\varOmega$ be a convex, open subset of $\mathbb{R}^n$ and let $\mathcal{D}'(\varOmega)$ be the space of distributions on $\varOmega$. It is shown that there exist linear embeddings of $\mathcal{D}'(\varOmega)$ into a differential algebra that commute with partial derivatives and that embed $\mathcal{C}^{\infty}(\varOmega)$ as a subalgebra. This embedding appears to be the first one after Colombeau’s to possess these properties. We show that many nonlinear operations on distributions can be defined that are not definable in the Colombeau setting.

AMS 2000 Mathematics subject classification: Primary 46F30. Secondary 13C11

Keywords

generalized functionsdistributionsembeddingsinjective modulesColombeau
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 46 , Issue 2 , June 2003 , pp. 373 - 378
Copyright
Copyright © Edinburgh Mathematical Society 2003