Recent progress in special Colombeau algebras: geometry, topology, and algebra

DOI10.4064/BC88-0-14zbMath1203.46051arXiv0712.4340OpenAlexW2963209762MaRDI QIDQ3567704

Michael Kunzinger

Publication date: 17 June 2010

Published in: Linear and Non-Linear Theory of Generalized Functions and its Applications (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/0712.4340

zbMATH Keywords

Colombeau algebrasnon-smooth differential geometry

Mathematics Subject Classification ID

Distributions and generalized functions on nonlinear spaces (46T30) Duality theory for topological vector spaces (46A20) Ideals in associative algebras (16D25) Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30)

Related Items (1)

Algebras of generalized functions with smooth parameter dependence

This page was built for publication: Recent progress in special Colombeau algebras: geometry, topology, and algebra