Seminars: D. Girela, Superposition operators on spaces of analytic functions

SEMINARS


Seminar on Analysis, Differential Equations and Mathematical Physics May 4, 2023 18:00, Rostov-on-Don, online, ссылка для подключения на странице семинара

Superposition operators on spaces of analytic functions D. Girela Department of Mathematics, University of Malaga
Abstract: If $\varphi $ is an entire function then the superposition operator $S_\varphi $ is defined by $$S_\varphi (f)(z)=\varphi \left (f(z)\right ),\quad f\in Hol (\mathbb D),\quad z\in \mathbb D.$$ If $X$ and $Y$ are two subspaces of $ Hol(\mathbb D)$, the question is: For which entire functions $\varphi$ does the operator $S_\varphi$ map $X$ into $Y$?, and when is continuous and/or bounded? This question has been solved for a good number of pairs $(X,\,Y)$ of spaces of analytic functions in the disc by distint authors including Cámera, Giménez, Buckley, Fernández, Bonet, Vukotic and others. After presenting some of these results, I will turn to deal with a number of contributions to the topic I have obtain in collaboration with some colleagues in the last few years. Language: English Website: https://msrn.tilda.ws/sl