Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 422, Issue 1, Pages 56-71Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2014.08.036
Keywords
Colombeau generalized functions; Strongly internal sets; Generalized smooth functions
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Funding
- Austrian Science Fund FWF [M1247-N13, P25116-N25, P23714, P25326]
- Research Foundation Flanders FWO [1.5.138.13N]
- Austrian Science Fund (FWF) [P 25326, P 25116, P 23714] Funding Source: researchfish
- Austrian Science Fund (FWF) [P25326, P25116, P23714] Funding Source: Austrian Science Fund (FWF)
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Based on a refinement of the notion of internal sets in Colombeau's theory, so-called strongly internal sets, we introduce the space of generalized smooth functions, a maximal extension of Colombeau generalized functions. Generalized smooth functions as morphisms between sets of generalized points form a sub-category of the category of topological spaces. In particular, they can be composed unrestrictedly. (C) 2014 Elsevier Inc. All rights reserved.
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