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http://hdl.handle.net/10077/31873
Title: | Some remarks on substitution and composition operators | Authors: | Appell, Jürgen López Brito, Belén Reinwann, Simon Schöller, Kilian |
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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