Geodesic
On the orbits of analytic functions with respect to a~Pommiez type operator
Ufa mathematical journal, Tome 7 (2015) no. 4, pp. 71-75

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Let $\Omega$ be a simply connected domain in the complex plane containing the origin, $A(\Omega)$ be the Fréchet space of all analytic on $\Omega$ functions. An analytic on $\Omega$ function $g_0$ such that $g_0(0)=1$ defines the Pommiez type operator which acts continuously and linearly in $A(\Omega)$. In this article we describe cyclic elements of the Pommiez type operator in space $A(\Omega)$. Similar results were obtained early for functions $g_0$ having no zeroes in domain $\Omega$.
Keywords: Pommiez operator, analytic function.
Mots-clés : cyclic element 
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O. A. Ivanova; S. N. Melikhov. On the orbits of analytic functions with respect to a~Pommiez type operator. Ufa mathematical journal, Tome 7 (2015) no. 4, pp. 71-75. http://geodesic.mathdoc.fr/item/UFA_2015_7_4_a5/