The Corona Property in Nevanlinna quotient algebras and interpolating sequences
Let I be an inner function in the unit disk D and let N denote the Nevanlinna class. We prove that under natural assumptions, Bézout equations in the quotient algebra N/IN can be solved if and only if the zeros of I form a finite union of Nevanlinna interpolating sequences. This is in contrast with...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:306152 |
| Acceso en línea: | https://ddd.uab.cat/record/306152 https://dx.doi.org/urn:doi:10.1016/j.jfa.2018.08.001 |
| Access Level: | acceso abierto |
| Palabra clave: | Corona problem Interpolating sequences Nevanlinna class Quotient algebras |
| Sumario: | Let I be an inner function in the unit disk D and let N denote the Nevanlinna class. We prove that under natural assumptions, Bézout equations in the quotient algebra N/IN 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. |
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