Year: 2020
Type: preprint
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 $Ω$ of the complex plane, containing the origin. In the case when the function, which defines this operator, is not has zeros in $Ω$ all such subspaces are finite-dimensional. If additionally $Ω$ coincides with the complex plane, then the considered operator is unicellular. If this function has zeros in $Ω$, 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.
Source: arXiv (Cornell University)
Authors: Ivanova, Olga A., Melikhov, Sergej N., Melikhov, Yurii N.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4307728976