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...

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Autores: Massaneda Clares, Francesc Xavier, Nicolau Nos, Artur, Thomas, Pascal J.
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
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spelling The Corona Property in Nevanlinna quotient algebras and interpolating sequencesMassaneda Clares, Francesc XavierNicolau Nos, ArturThomas, Pascal J.Teoria de NevanlinnaFuncions de variables complexesTeoria geomètrica de funcionsNevanlinna theoryFunctions of complex variablesGeometric function theoryLet $I$ 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.Elsevier2023202320192023info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersion26 p.application/pdfapplication/pdfhttps://hdl.handle.net/2445/192389Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésVersió postprint del document publicat a: https://doi.org/10.1016/j.jfa.2018.08.001Journal of Functional Analysis, 2019, vol. 276, num. 8, p. 2636-2661https://doi.org/10.1016/j.jfa.2018.08.001cc-by-nc-nd (c) Elsevier, 2019https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:2445/1923892026-05-29T05:05:01Z
dc.title.none.fl_str_mv The Corona Property in Nevanlinna quotient algebras and interpolating sequences
title The Corona Property in Nevanlinna quotient algebras and interpolating sequences
spellingShingle The Corona Property in Nevanlinna quotient algebras and interpolating sequences
Massaneda Clares, Francesc Xavier
Teoria de Nevanlinna
Funcions de variables complexes
Teoria geomètrica de funcions
Nevanlinna theory
Functions of complex variables
Geometric function theory
title_short The Corona Property in Nevanlinna quotient algebras and interpolating sequences
title_full The Corona Property in Nevanlinna quotient algebras and interpolating sequences
title_fullStr The Corona Property in Nevanlinna quotient algebras and interpolating sequences
title_full_unstemmed The Corona Property in Nevanlinna quotient algebras and interpolating sequences
title_sort The Corona Property in Nevanlinna quotient algebras and interpolating sequences
dc.creator.none.fl_str_mv Massaneda Clares, Francesc Xavier
Nicolau Nos, Artur
Thomas, Pascal J.
author Massaneda Clares, Francesc Xavier
author_facet Massaneda Clares, Francesc Xavier
Nicolau Nos, Artur
Thomas, Pascal J.
author_role author
author2 Nicolau Nos, Artur
Thomas, Pascal J.
author2_role author
author
dc.subject.none.fl_str_mv Teoria de Nevanlinna
Funcions de variables complexes
Teoria geomètrica de funcions
Nevanlinna theory
Functions of complex variables
Geometric function theory
topic Teoria de Nevanlinna
Funcions de variables complexes
Teoria geomètrica de funcions
Nevanlinna theory
Functions of complex variables
Geometric function theory
description 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.
publishDate 2019
dc.date.none.fl_str_mv 2019
2023
2023
2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/192389
url https://hdl.handle.net/2445/192389
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a: https://doi.org/10.1016/j.jfa.2018.08.001
Journal of Functional Analysis, 2019, vol. 276, num. 8, p. 2636-2661
https://doi.org/10.1016/j.jfa.2018.08.001
dc.rights.none.fl_str_mv cc-by-nc-nd (c) Elsevier, 2019
https://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by-nc-nd (c) Elsevier, 2019
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 26 p.
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.812429

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