The Corona Property in Nevanlinna quotient algebras and interpolating sequences
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 Nevanlinn...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/192389 |
| Acceso en línea: | https://hdl.handle.net/2445/192389 |
| Access Level: | acceso abierto |
| Palabra clave: | Teoria de Nevanlinna Funcions de variables complexes Teoria geomètrica de funcions Nevanlinna theory Functions of complex variables Geometric function theory |
| Sumario: | 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. |
|---|