4.2 Article

A CONVENIENT NOTION OF COMPACT SET FOR GENERALIZED FUNCTIONS

Journal

Publisher

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

  1. Austrian Science Fund FWF [P25116, P25311, P23714, P25326]
  2. Austrian Science Fund (FWF) [P 25116, P 23714] Funding Source: researchfish
  3. 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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