A Convenient Notion of Compact Set for Generalized Functions

Author:

Giordano Paolo,Kunzinger Michael

Abstract

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.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference31 articles.

1. Colombeau's generalized functions: topological structures; microlocal properties. A simplified point of view, I;Scarpalɉzos;Bull. Cl. Sci. Math. Nat. Sci. Math.,2000

2. Spherical completeness of the non-Archimedean ring of Colombeau generalized numbers;Mayerhofer;Bull. Inst. Math. Acad. Sin. (N.S.),2007

3. On duality theory and pseudodifferential techniques for Colombeau algebras: generalized delta functionals, kernels and wave front sets

4. Characterization of colombeau generalized functions by their pointvalues

5. Natural topologies on Colombeau algebras

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