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Article Dans Une Revue Journal of Functional Analysis Année : 2019

The Corona Property in Nevanlinna quotient algebras and Interpolating sequences

Résumé

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.
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Dates et versions

hal-01766910 , version 1 (15-05-2024)

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Pascal J. Thomas, Xavier Massaneda, Artur Nicolau. The Corona Property in Nevanlinna quotient algebras and Interpolating sequences. Journal of Functional Analysis, 2019, 276, pp.2636-2661. ⟨10.1016/j.jfa.2018.08.001⟩. ⟨hal-01766910⟩
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