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On regularization of vector distributions on manifolds

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Published/Copyright: May 5, 2016

Abstract

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.

MSC 2010: 46T30; 46A32

Communicated by Karl-Hermann Neeb


Funding source: Austrian Science Fund

Award Identifier / Grant number: P26859-N25

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

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Received: 2015-9-2
Revised: 2016-2-18
Published Online: 2016-5-5
Published in Print: 2016-11-1

© 2016 by De Gruyter

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