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Abstract
© 2018 Elsevier Inc. 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.
Original language  English 

Pages (fromto)  26362661 
Journal  Journal of Functional Analysis 
Volume  276 
DOIs  
Publication status  Published  15 Apr 2019 
Keywords
 Corona problem
 Interpolating sequences
 Nevanlinna class
 Quotient algebras
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Dive into the research topics of 'The Corona Property in Nevanlinna quotient algebras and interpolating sequences'. Together they form a unique fingerprint.Projects
 1 Finished

Aspectos probabilísticos y geométricos de la teoría de funciones
Nicolau Nos, A., Gonzalez Llorente, J., Arroyo Garcia, A. R., Donaire Benito, J. J., Soler Gibert, O., González Fuentes, M. J., Levi, M., Limani, A. & Macia Medina, V. J.
Ministerio de Ciencia e Innovación (MICINN)
1/01/18 → 30/09/22
Project: Research Projects and Other Grants