☆ 4.4 Article

Point value characterizations and related results in the full Colombeau algebras Ge(Ω) and Gd(Ω)

MATHEMATISCHE NACHRICHTEN (2013)

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Journal

MATHEMATISCHE NACHRICHTEN
Volume 286, Issue 10, Pages 1007-1021

Publisher

WILEY-V C H VERLAG GMBH
DOI: 10.1002/mana.200910280

Keywords

Diffeomorphism invariant Colombeau algebra; point value characterization; pointvalues; algebras of generalized functions; invertibility of generalized functions; generalized numbers; MSC (2010); 46F30

Categories

Mathematics

Funding

  1. START-project of the Austrian Science Fund [Y237, P20525]
  2. Doctoral College Differential Geometry and Lie Groups of the University of Vienna
  3. Austrian Science Fund (FWF) [P23714] Funding Source: Austrian Science Fund (FWF)

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We present a point value characterization for elements of the elementary full Colombeau algebra G(e)(Omega) and the diffeomorphism invariant full Colombeau algebra G(d)(Omega). Moreover, several results from the special algebra G(s)(Omega) about generalized numbers and invertibility are extended to the elementary full algebra.

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