Topics on nonlinear generalized functions
J.F. Colombeau
TL;DR
This paper provides an overview of nonlinear generalized functions, their connections to distribution theory, applications, and recent advances in their topological and functional analysis properties.
Contribution
It summarizes recent developments in nonlinear generalized functions, including their theoretical foundations, applications, and new topological and functional analysis perspectives.
Findings
Connections with distribution theory clarified
Examples of applications demonstrated
New topological and functional analysis results obtained
Abstract
The aim of this paper is to give the text of a recent introduction to nonlinear generalized functions exposed in my talk in the congress gf2011, which was asked by several participants. Three representative topics were presented: two recalls "Nonlinear generalized functions and their connections with distribution theory", "Examples of applications", and a recent development: "Locally convex topologies and compactness: a functional analysis of nonlinear generalized functions".
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Taxonomy
TopicsMathematical and Theoretical Analysis · Mathematical Analysis and Transform Methods · Advanced Topology and Set Theory