The chain rule as a functional equation
type: Item
instance of: scholarly article
title: The chain rule as a functional equation
zbMATH Open document ID: 1203.39014
author: S. Artstein-Avidan
author: Hermann König
author: Vitali Milman
published in: Journal of Functional Analysis
publication date: 2010-11-03T00:00:00Z
review text: Motivated by the classical chain rule of the derivative \(D: C^1 (\mathbb R) \to C(\mathbb R)\), \(D(f \circ g) = ((Df)\circ g)\cdot Dg\), the authors study the general functional equation \(T(f \circ g) = (Tf) \circ g \cdot Tg\) for various classes of operators \(T\) from \(C^1(\mathbb R) \) into \(C(\mathbb R)\), or in other domains like \(C^k (\mathbb R)\). Some generalized forms are also studied.
reviewed by: Claudi Alsina
Mathematics Subject Classification ID: 39B42
Mathematics Subject Classification ID: 39B22
zbMATH DE Number: 5809717
zbMATH Keywords: chain rule
zbMATH Keywords: functional equation
MaRDI profile type: Publication
full work available at URL: j.jfa.2010.07.002
OpenAlex ID: W2028062149
cites work: Q5322210
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cites work: Q3671563
DOI: 10.1016/J.JFA.2010.07.002
description: scientific article; zbMATH DE number 5809717