Article

    Ufa Mathematical Journal
    Volume 7, Number 4, pp. 71-75

    On the orbits of analytic functions with respect to a Pommiez type operator


    Ivanova О.А., Melikhov S.N.

    DOI:10.13108/2015-7-4-71

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    Abstact


    Let $\Omega$ be a simply connected domain in the complex plane containing the origin, $A(\Omega)$ be the Fréchet space of all functions analytic in $\Omega$. A function $g_0$ analytic in $\Omega$ 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 $\Omega$.