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Title: | The Corona Property in Nevanlinna quotient algebras and interpolating sequences |
Author: | Massaneda Clares, Francesc Xavier Nicolau Nos, Artur Thomas, Pascal J. |
Keywords: | Teoria de Nevanlinna Funcions de variables complexes Teoria geomètrica de funcions Nevanlinna theory Functions of complex variables Geometric function theory |
Issue Date: | 15-Apr-2019 |
Publisher: | Elsevier |
Abstract: | Let $I$ be an inner function in the unit disk $\mathbb{D}$ and let $\mathcal{N}$ denote the Nevanlinna class. We prove that under natural assumptions, Bezout equations in the quotient algebra $\mathcal{N} / I \mathcal{N}$ can be solved if and only if the zeros of $I$ form a finite union of Nevanlinna interpolating sequences. This is in contrast with the situation in the algebra of bounded analytic functions, where being a finite union of interpolating sequences is a sufficient but not necessary condition. An analogous result in the Smirnov class is proved as well as several equivalent descriptions of Blaschke products whose zeros form a finite union of interpolating sequences in the Nevanlinna class. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1016/j.jfa.2018.08.001 |
It is part of: | Journal of Functional Analysis, 2019, vol. 276, num. 8, p. 2636-2661 |
URI: | http://hdl.handle.net/2445/192389 |
Related resource: | https://doi.org/10.1016/j.jfa.2018.08.001 |
ISSN: | 0022-1236 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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