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Full and Special Colombeau Algebras

Part of: Distributions, generalized functions, distribution spaces

Published online by Cambridge University Press:  13 June 2018

M. Grosser  and
E. A. Nigsch
M. Grosser
Affiliation:
Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria (michael.grosser@univie.ac.at)
E. A. Nigsch
Affiliation:
Wolfgang-Pauli-Institut, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria (eduard.nigsch@univie.ac.at)
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Abstract

We introduce full diffeomorphism-invariant Colombeau algebras with added ε-dependence in the basic space. This unites the full and special settings of the theory into one single framework. Using locality conditions we find the appropriate definition of point values in full Colombeau algebras and show that special generalized points suffice to characterize elements of full Colombeau algebras. Moreover, we specify sufficient conditions for the sheaf property to hold and give a definition of the sharp topology in this framework.

Keywords

Colombeau algebrageneralized functionfullspecialsharp topologypoint valueslocalitysheaf property

MSC classification

Primary: 46F30: Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 61 , Issue 4 , November 2018 , pp. 961 - 994
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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