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Zeitschrift für Analysis und ihre Anwendungen


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Volume 33, Issue 1, 2014, pp. 119–123
DOI: 10.4171/ZAA/1502

Published online: 2013-12-27

A Note on the Composition of Regular Functions

Wadie Aziz[1], Nelson Merentes[2] and José Luis Sánchez[3]

(1) Universidad de los Andes, Trujillo, Venezuela
(2) Central University of Venezuela, Caracas, Venezuela
(3) Central University of Venezuela, Caracas, Venezuela

In this note we give a condition on a function $h:\mathbb{R}\rightarrow\mathbb{R}$, both necessary and sufficient, under which the nonlinear composition operator $Hf = h \circ f$ maps the space of all regular functions $f : [a,b] \rightarrow \mathbb{R}$ into itself. Moreover, we show that in this case the operator $H$ is automatically bounded in the supremum norm.

Keywords: Regular functions, composition operators, Sierpinski decomposition

Aziz Wadie, Merentes Nelson, Sánchez José Luis: A Note on the Composition of Regular Functions. Z. Anal. Anwend. 33 (2014), 119-123. doi: 10.4171/ZAA/1502