The Corona Property in Nevanlinna quotient algebras and interpolating sequences

Xavier Massaneda, Artur Nicolau, Pascal J. Thomas

Research output: Contribution to journalArticleResearch

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)2636-2661
JournalJournal of Functional Analysis
Volume276
DOIs
Publication statusPublished - 15 Apr 2019

Keywords

  • Corona problem
  • Interpolating sequences
  • Nevanlinna class
  • Quotient algebras

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