Jürgen Appell, Substitution and composition operators: The expected and unexpected, Vol. 2024 (2024), Article ID 7, pp. 1-10

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DOI: 10.23952/cot.2024.7

Received May 20, 2023; Accepted July 16, 2023; Published online October 24, 2023

Abstract. We give continuity and compactness conditions for the linear substitution operator $S_{\varphi}(f)(t):=f(\varphi(t))$ and the nonlinear composition operator $C_g(f)(x) := g(f(x))$ , in terms of the generating functions $\varphi : [0, 1]\rightarrow [0, 1]$ resp. $g : \mathbb{R} \rightarrow \mathbb{R}$ , with a particular emphasis on examples and counterexamples.

How to Cite this Article:
J. Appell, Substitution and composition operators: The expected and unexpected, Commun. Optim. Theory 2024 (2024) 7.