Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/31873
Title: Some remarks on substitution and composition operators
Authors: Appell, Jürgen
López Brito, Belén
Reinwand, Simon
Schöller, Kilian
Keywords: Substitution operatorscomposition operatorsinjectivitysurjectivitycontinuous functionsLipschitz functionsfunctions of bounded variationBaire one functions
Issue Date: 2021
Publisher: EUT Edizioni Università di Trieste
Source: Jürgen Appell, Bélen López Brito, Simon Reinwann, Kilian Schöller, "Some remarks on substitution and composition operators" in: "Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.53 (2021)", EUT Edizioni Università di Trieste, Trieste, 2021. pp. 25
Journal: Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics 
Abstract: 
In this paper we study the linear substitution operator
Sϕ(f) := f ◦ ϕ generated by some function ϕ : [0, 1] → [0, 1], as well as the nonlinear composition operator Cg(f) := g ◦ f generated by some
function g : R → R. We will show that these operators have a very different (and sometimes quite surprising) behavior in the space of con-tinuous functions, Lipschitz functions, functions of bounded variation, and Baire class one functions. A main emphasis is put on examples and counterexamples which illustrate this behavior.
Type: Article
URI: http://hdl.handle.net/10077/31873
ISSN: 0049-4704
eISBN: 2464-8728
DOI: 10.13137/2464-8728/31873
Rights: Attribution-NonCommercial-NoDerivatives 4.0 Internazionale
Appears in Collections:Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.53 (2021)

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