Recent Progress in Special Colombeau Algebras: Geometry, Topology, and Algebra

Details Recent Progress in Special Colombeau Algebras: Geometry, Topology, and Algebra Recent Progress in Special Colombeau Algebras: Geometry, Topology, and Algebra

2007-12-28

arxiv.org/abs/0712.4340v1

Mathematics

Functional Analysis

12 pages, contribution for conference "Generalized Functions 2007", Banach Center, Bedlewo, Poland

Scientific paper

Over the past few years there has been considerable progress in the structural understanding of special Colombeau algebras. We present some of the main trends in this development: non-smooth differential geometry, locally convex theory of modules over the ring of generalized numbers, and algebraic aspects of Colombeau theory. Some open problems are given and directions of further research are outlined.

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