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Volume 28, Issue 6


On regularization of vector distributions on manifolds

Eduard A. Nigsch
Published Online: 2016-05-05 | DOI: https://doi.org/10.1515/forum-2015-0067


One can represent Schwartz distributions with values in a vector bundle E by smooth sections of E with distributional coefficients. Moreover, any linear continuous operator which maps E-valued distributions to smooth sections of another vector bundle F can be represented by sections of the external tensor product E*F with coefficients in the space (𝒟,C) of operators from scalar distributions to scalar smooth functions. We establish these isomorphisms topologically, i.e., in the category of locally convex modules, using category theoretic formalism in conjunction with L. Schwartz’ notion of ε-product.

Keywords: Vector-valued distributions; distributions on manifolds; topological tensor product,regularization

MSC 2010: 46T30; 46A32


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About the article

Received: 2015-09-02

Revised: 2016-02-18

Published Online: 2016-05-05

Published in Print: 2016-11-01

Funding Source: Austrian Science Fund

Award identifier / Grant number: P26859-N25

This work was supported by the Austrian Science Fund (FWF) grant P26859-N25.

Citation Information: Forum Mathematicum, Volume 28, Issue 6, Pages 1131–1141, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2015-0067.

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