Characterization of the Schur class in terms of the coefficients of a series on the Laguerre basis
| Autor: | V. V. Savchuk, M. V. Savchuk |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Reports of the National Academy of Sciences of Ukraine. :9-15 |
| ISSN: | 2518-153X 1025-6415 |
| DOI: | 10.15407/dopovidi2020.11.009 |
| Popis: | The classical Schur criterion answers the question of whether a function f given by its power series f(x)=∑k=0∞CkZk is a Schur function that is, holomorphic in a unit disk D and such that supz∈D | f (z) | ≤ 1. Regarding this criterion, there are a large number of completed results devoted to its generalizations and various applications, but, as it seems to us, there is no criterion for a complete description of the Schur class in terms of coefficients of orthogonal series on arbitrary complete orthonormal systems. In this paper, we formulate such criterion for a formal orthogonal series with complex coefficients based on the Laguerre system. |
| Databáze: | OpenAIRE |
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