Composing infinitely differentiable functions
type: Item
instance of: scholarly article
title: Composing infinitely differentiable functions
zbMATH Open document ID: 0712.47054
DOI: 10.1007/BF02571371
author: Jürgen Appell
author: V. I. Nazarov
author: Peter P. Zabreĭko
published in: Mathematische Zeitschrift
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174252
review text: Given a Banach space X and a smooth function f: [a,b]\(\times X\to X\), we provide necessary and sufficient conditions under which the nonlinear superposition operator \(Fx(s)=f(s,x(s))\) acts between two Roumieu classes \(R_{\mu}(L,X)\) and \(R_{\mu}(L',X)\), or between the projective and inductive limits \(R_{\mu}(0,X)\) and \(R_{\mu}(\infty,X)\), respectively. Moreover, we discuss some boundedness, continuity, and compactness properties of F in such spaces.
reviewed by: Jürgen Appell
Mathematics Subject Classification ID: 47H30
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 46F05
Mathematics Subject Classification ID: 46E15
zbMATH DE Number: 4171783
zbMATH Keywords: nonlinear superposition operator
zbMATH Keywords: Roumieu classes
zbMATH Keywords: projective and inductive limits
zbMATH Keywords: boundedness
zbMATH Keywords: continuity
zbMATH Keywords: compactness properties
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4171783