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This article is cited in 4 scientific papers (total in 4 papers)
On the orbits of analytic functions with respect to a Pommiez type operator
O. A. Ivanovaa, S. N. Melikhovab a Institute of Mathematics, Mechanics and Computer Sciences, Southern Federal University, Rostov-on-Don, Russia
b Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz, Russia
Abstract:
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, cyclic element, analytic function.
Received: 14.05.2015
Citation:
O. A. Ivanova, S. N. Melikhov, “On the orbits of analytic functions with respect to a Pommiez type operator”, Ufimsk. Mat. Zh., 7:4 (2015), 75–79; Ufa Math. J., 7:4 (2015), 71–75
Linking options:
https://www.mathnet.ru/eng/ufa302https://doi.org/10.13108/2015-7-4-71 https://www.mathnet.ru/eng/ufa/v7/i4/p75
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Abstract page: | 388 | Russian version PDF: | 133 | English version PDF: | 18 | References: | 94 |
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