2018/04/10 by Massaneda, Xavier, Nicolau, Artur, Thomas, Pascal J.
#30H15 #30H80 #30J10 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.1804.03536
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.