Journal
FORUM MATHEMATICUM
Volume 28, Issue 6, Pages 1131-1141Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/forum-2015-0067
Keywords
Vector-valued distributions; distributions on manifolds; topological tensor product; regularization
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Funding
- Austrian Science Fund (FWF) grant [P26859-N25]
- Austrian Science Fund (FWF) [P23714, P26859] Funding Source: Austrian Science Fund (FWF)
- Austrian Science Fund (FWF) [P 23714] Funding Source: researchfish
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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* boxed times F with coefficients in the space L(D', C-infinity) 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 epsilon-product.
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