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Monatshefte für Mathematik

, Volume 166, Issue 3–4, pp 361–370 | Cite as

An algebraic approach to manifold-valued generalized functions

  • Annegret BurtscherEmail author
Article
  • 49 Downloads

Abstract

We discuss the nature of structure-preserving maps of varies function algebras. In particular, we identify isomorphisms between special Colombeau algebras on manifolds with invertible manifold-valued generalized functions in the case of smooth parametrization. As a consequence, and to underline the consistency and validity of this approach, we see that this generalized version on algebra isomorphisms in turn implies the classical result on algebras of smooth functions.

Keywords

Nonlinear generalized functions Special Colombeau algebras Algebra homomorphisms Smooth functions Diffeomorphisms 

Mathematics Subject Classification (2000)

46F30 46E25 46T30 54C40 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Faculty of MathematicsUniversity of ViennaViennaAustria

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