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arXiv · 2005.01596

Invariant subspaces of a generalized backward shift operator and rational functions

Olga A. Ivanova·Sergej N. Melikhov·Yurii N. Melikhov
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Abstract

We obtaine the full characterization of proper closed invariant subspaces of a generalized backward shift operator (Pommiez operator) in the Frechet space of all holomorphic functions on a simply connected domain $\Omega$ of the complex plane, containing the origin. In the case when the function, which defines this operator, is not has zeros in $\Omega$ all such subspaces are finite-dimensional. If additionally $\Omega $ coincides with the complex plane, then the considered operator is unicellular. If this function has zeros in $\Omega $, then the family of mentioned invariant subspaces splits into two classes: the first consists of finite-dimensional subspaces, and the second of infinite-dimensional ones.

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Olga A. Ivanova, Sergej N. Melikhov, Yurii N. Melikhov. 2020-05-04. Invariant subspaces of a generalized backward shift operator and rational functions. https://arxiv.org/abs/2005.01596

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