Abstract:
Let Ω be a simply connected domain in the complex plane containing the origin, A(Ω) be the Fréchet space of all analytic on Ω functions. An analytic on Ω function g0 such that g0(0)=1 defines the Pommiez type operator which acts continuously and linearly in A(Ω). In this article we describe cyclic elements of the Pommiez type operator in space A(Ω). Similar results were obtained early for functions g0 having no zeroes in domain Ω.
Citation:
O. A. Ivanova, S. N. Melikhov, “On the orbits of analytic functions with respect to a Pommiez type operator”, Ufa Math. J., 7:4 (2015), 71–75
\Bibitem{IvaMel15}
\by O.~A.~Ivanova, S.~N.~Melikhov
\paper On the orbits of analytic functions with respect to a~Pommiez type operator
\jour Ufa Math. J.
\yr 2015
\vol 7
\issue 4
\pages 71--75
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\crossref{https://doi.org/10.13108/2015-7-4-71}
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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:
O. A. Ivanova, S. N. Melikhov, Yu. N. Melikhov, “Invariant subspaces of the generalized backward shift operator and rational functions”, St. Petersburg Math. J., 33:6 (2022), 927–942
S. N. Melikhov, “Coefficients of exponential series for analytic functions and the Pommiez operator”, J. Math. Sci. (N. Y.), 257:2 (2021), 206–245
P. A. Ivanov, S. N. Melikhov, “Pommier Operator in Spaces of Analytic Functions of Several Complex Variables”, J. Math. Sci. (N. Y.), 252:3 (2021), 345–359
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
Citation in format AMSBIB
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