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Ufimsk. Mat. Zh., 2015, Volume 7, Issue 4, Pages 75–79 (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

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.

Full text: PDF file (395 kB)
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English version:
Ufa Mathematical Journal, 2015, 7:4, 71–75 (PDF, 288 kB); https://doi.org/10.13108/2015-7-4-71

Bibliographic databases:

UDC: 517.9
MSC: 47A16, 47B38, 46E10
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

Citation in format AMSBIB
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\pages 75--79
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O. A. Ivanova, S. N. Melikhov, “On the Completeness of Orbits of a Pommiez Operator in Weighted (LF)-Spaces of Entire Functions”, Complex Anal. Oper. Theory, 11:6 (2017), 1407–1424  crossref  mathscinet  zmath  isi  scopus
    2. P. A. Ivanov, S. N. Melikhov, “Operator Pomme v prostranstvakh analiticheskikh funktsii mnogikh kompleksnykh peremennykh”, Kompleksnyi analiz, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 153, VINITI RAN, M., 2018, 55–68  mathnet  mathscinet
    3. S. N. Melikhov, “Koeffitsienty ryadov eksponent dlya analiticheskikh funktsii i operator Pomme”, Kompleksnyi analiz. Tselye funktsii i ikh primeneniya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 161, VINITI RAN, M., 2019, 65–103  mathnet  mathscinet
    4. O. A. Ivanova, S. N. Melikhov, Yu. N. Melikhov, “Invariantnye podprostranstva operatora obobschennogo obratnogo sdviga i ratsionalnye funktsii”, Algebra i analiz, 33:6 (2021), 49–70  mathnet
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