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arXiv · 1804.03536

The Corona Property in Nevanlinna quotient algebras and Interpolating sequences

Xavier Massaneda·Artur Nicolau·Pascal J. Thomas
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Abstract

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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Xavier Massaneda, Artur Nicolau, Pascal J. Thomas. 2018-04-10. The Corona Property in Nevanlinna quotient algebras and Interpolating sequences. https://arxiv.org/abs/1804.03536

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