, Volume 129, Issue 1, pp 1-14

Topology on Asymptotic Algebras of Generalized Functions and Applications

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Abstract.

 Starting from a locally convex metrisable topological space and from any asymptotic scale, we construct a generalized extension of this space. To those extensions, we associate Hausdorff topologies. We introduce the notion of a temperate map, with respect to a given asymptotic scale, between two locally convex metrisable semi-normed spaces. We show that such mappings extend in a canonical way to mappings between the respective generalized extensions. We give an application to nonlinear Dirichlet boundary value problems with singular data in the framework of generalized extensions.

(Received 2 November 1998; in revised form 25 February 1999)