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Ufa Mathematical Journal, 2015, Volume 7, Issue 4, Pages 71–75
DOI: https://doi.org/10.13108/2015-7-4-71
(Mi ufa302)
 

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
References:
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
Russian version:
Ufimskii Matematicheskii Zhurnal, 2015, Volume 7, Issue 4, Pages 75–79
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 47A16, 47B38, 46E10
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
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\pages 75--79
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Linking options:
  • https://www.mathnet.ru/eng/ufa302
  • https://doi.org/10.13108/2015-7-4-71
  • https://www.mathnet.ru/eng/ufa/v7/i4/p75
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Уфимский математический журнал
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    Abstract page:388
    Russian version PDF:133
    English version PDF:18
    References:94
     
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