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Some remarks on substitution and composition operators
Appell, Jürgen
López Brito, Belén
Reinwand, Simon
Schöller, Kilian
2021
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e-ISBN
2464-8728
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.
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
Languages
en
Rights
Attribution-NonCommercial-NoDerivatives 4.0 Internazionale
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