Monatshefte für Mathematik

, Volume 129, Issue 1, pp 1–14 | Cite as

Topology on Asymptotic Algebras of Generalized Functions and Applications

  • Antoine Delcroix
  • Dimitris Scarpalezos

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.

1991 Mathematics Subject Classification: 26E99, 34E10, 35D99, 46F99 
Key words: Generalized functions, asymptotic scale Dirichlet problem, singular data sharp topology 

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Copyright information

© Springer-Verlag Wien 2000

Authors and Affiliations

  • Antoine Delcroix
    • 1
  • Dimitris Scarpalezos
    • 2
  1. 1.IUFM des Antilles et de la Guyane, Pointe-à-Pitre, GuadeloupeGP
  2. 2.Université de Paris 7, FranceFR

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