On the orbits of analytic functions with respect to a Pommiez type operator
Об орбитах аналитических функций относительно оператора типа Поммье

Olga Aleksandrovna Ivanova, Sergej Nikolaevich Melikhov
2015 Ufimskii Matematicheskii Zhurnal  
Let Ω be a simply connected domain in the complex plane containing the origin, (Ω) be the Fréchet space of all functions analytic in Ω. A function 0 analytic in Ω such that 0 (0) = 1 defines the Pommiez type operator which acts continuously and linearly in (Ω). In this article we describe cyclic elements of the Pommiez type operator in space (Ω). Similar results were obtained early for functions 0 having no zeroes in domain Ω.
doi:10.13108/2015-7-4-71 fatcat:zgzf4v2b2jdl7nxjracoxmn64a