Journal
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY
Volume 61, Issue 1, Pages 57-92Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S0013091516000559
Keywords
functionally compact sets; Colombeau generalized functions; generalized smooth functions; locally convex modules
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Funding
- Austrian Science Fund FWF [P25116, P25311, P23714, P25326]
- Austrian Science Fund (FWF) [P 25116, P 23714] Funding Source: researchfish
- Austrian Science Fund (FWF) [P25116, P25311, P25326] Funding Source: Austrian Science Fund (FWF)
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We introduce the notion of functionally compact sets into the theory of nonlinear generalized functions in the sense of Colombeau. The motivation behind our construction is to transfer, as far as possible, properties enjoyed by standard smooth functions on compact sets into the framework of generalized functions. Based on this concept, we introduce spaces of compactly supported generalized smooth functions that are close analogues to the test function spaces of distribution theory. We then develop the topological and functional-analytic foundations of these spaces.
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