Strongly internal sets and generalized smooth functions
type: Item
instance of: scholarly article
title: Strongly internal sets and generalized smooth functions
zbMATH Open document ID: 1328.46037
author: Paolo Giordano
author: Michael Kunzinger
author: Hans Vernaeve
published in: Journal of Mathematical Analysis and Applications
publication date: 2014-10-07T00:00:00Z
full work available at URL: https://arxiv.org/abs/1402.3534
reviewed by: Biljana Tome Jolevska-Tuneska
Mathematics Subject Classification ID: 46F30
zbMATH DE Number: 6351981
zbMATH Keywords: Colombeau generalized functions
zbMATH Keywords: strongly internal sets
zbMATH Keywords: generalized smooth functions
MaRDI profile type: Publication
OpenAlex ID: W2962710273
arXiv ID: 1402.3534
Wikidata QID: Q59310068
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DOI: 10.1016/J.JMAA.2014.08.036
review text: The authors introduce a generalization of Colombeau-type generalized functions, which they call generalized smooth functions,NEWLINEGSF. These functions are set-theoretic maps on sets of generalized points that satisfy the minimal logical conditions necessary to obtain well-defined maps obeying the standard asymptotic estimates of the Colombeau approach. They are the natural extension of Colombeau generalized functions to general domains and they display optimal set-theoretical properties. The authors give proofs that GSF functions are locally Lipschitz functions. Also, this notion is studied for functions defined on and valued in generalized points.
description: scientific article; zbMATH DE number 6351981