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An algebraic approach to manifold-valued generalized functions

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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.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Vienna, Nordbergstraße 15, 1090, Vienna, Austria

    Annegret Burtscher

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  1. Annegret Burtscher
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Correspondence to Annegret Burtscher.

Additional information

This work was supported by project P20525 of the Austrian Science Fund (FWF) and research stipend FS 506/2010 from the University of Vienna.

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Burtscher, A. An algebraic approach to manifold-valued generalized functions. Monatsh Math 166, 361–370 (2012). https://doi.org/10.1007/s00605-011-0317-1

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  • DOI: https://doi.org/10.1007/s00605-011-0317-1

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