Superposition operators in the algebra of functions of two variables with finite total variation
type: Item
instance of: scholarly article
title: Superposition operators in the algebra of functions of two variables with finite total variation
zbMATH Open document ID: 1033.26019
published in: Monatshefte für Mathematik
publication date: 2002-12-01T00:00:00Z
review text: The author studies the Nemytskij operator \((Hf)(x) = h(x,f(x))\) in the space of functions \(f : [a,b]\times [c,d]\to\mathbb{R}\) of bounded variation. In particular, he shows that a Lipschitz condition for \(H\) in the norm of this space leads to a (mild or strong) degeneracy of the generating function \(h\). This extends previous results of the author [J. Appl. Anal. 6, 173--186 (2000; Zbl 0997.47051), Positivity 5, 323--358 (2001; Zbl 1027.47046), and J. Math. Sci., New York 111, 3387--3429 (2002; Zbl 1033.26014)]{} and by many other authors.
Mathematics Subject Classification ID: 26B30
Mathematics Subject Classification ID: 47H30
Mathematics Subject Classification ID: 26B40
Mathematics Subject Classification ID: 39B22
zbMATH DE Number: 1837389
zbMATH Keywords: functions of two variables
zbMATH Keywords: finite total variation
zbMATH Keywords: superposition operators
zbMATH Keywords: Nemytskij operator
author: V. V. Chistyakov
reviewed by: Jürgen Appell
MaRDI profile type: Publication
full work available at URL: s006050200048
OpenAlex ID: W1975275932
DOI: 10.1007/S006050200048
description: scientific article; zbMATH DE number 1837389