The operator of inversion as an everywhere continuous nowhere differentiable function
type: Item
instance of: scholarly article
title: The operator of inversion as an everywhere continuous nowhere differentiable function
zbMATH Open document ID: 0972.47051
DOI: 10.1007/BF03322011
author: Gyula Farkas
author: Barnabas M. Garay
published in: Results in Mathematics
publication date: 2001-05-13T00:00:00Z
review text: The authors give an interesting survey on smoothness properties of the inversion operator between various spaces of continuously differentiable functions. The behaviour of this operator exhibits many surprises; for example, it is continuous but nowhere differentiable beyong a certain ``critical'' order. This essentially completes and extends previous work of, e.g., K. P. Rybakowski and R. M. Dudley. The authors seem to be unaware, however, of related work by M. Lanza de Cristoforis.
Mathematics Subject Classification ID: 47H30
Mathematics Subject Classification ID: 58C20
Mathematics Subject Classification ID: 05C30
Mathematics Subject Classification ID: 46G05
zbMATH DE Number: 1563151
zbMATH Keywords: smoothness properties of the inversion operator
zbMATH Keywords: spaces of continuously differentiable functions
reviewed by: Jürgen Appell
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03322011
OpenAlex ID: W1980877956
description: scientific article; zbMATH DE number 1563151