Transformations of functions
type: Item
instance of: scholarly article
title: Transformations of functions
zbMATH Open document ID: 0588.26006
author: James Foran
published in: Real Analysis Exchange
publication date: 1984-01-01T00:00:00Z
review text: Consider the following problem: Let A be a class of real-valued functions defined on the line. What is the class \({\mathcal H}{\mathcal A}=\{h\circ f;\quad h\quad is\quad a\quad \hom eomorphism\quad and\quad f\in {\mathcal A}\}?\) The author gives a survey of known results for such classes \({\mathcal A}\), like the class of functions of bounded variation, absolutely continuous or differentiable functions, etc. Then he shows the difficulties connected with the characterization of other classes and proves certain auxiliary results. The paper contains interesting ideas and also some open problems.
Mathematics Subject Classification ID: 26A99
Mathematics Subject Classification ID: 26A15
Mathematics Subject Classification ID: 26A21
Mathematics Subject Classification ID: 26A24
Mathematics Subject Classification ID: 26A30
Mathematics Subject Classification ID: 26A45
Mathematics Subject Classification ID: 26A46
zbMATH DE Number: 3944183
zbMATH Keywords: transformations
zbMATH Keywords: absolutely continuous functions
zbMATH Keywords: homeomorphism
zbMATH Keywords: functions of bounded variation
zbMATH Keywords: differentiable functions
reviewed by: Jaroslav Smítal
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3944183