Nevanlinna classes associated to a closed set on $\partial$D

TL;DR

This paper introduces new Nevanlinna classes linked to boundary sets of the unit disc, providing alternative proofs of existing theorems and applications to eigenvalues of non-self-adjoint Schrödinger operators.

Contribution

It defines novel Nevanlinna classes associated with boundary sets and establishes Blaschke type theorems using several complex variables methods, offering new insights and proofs.

Findings

New Nevanlinna classes associated with boundary sets

Blaschke type theorems proved using complex variables methods

Applications to eigenvalues of non-self-adjoint Schrödinger operators

Abstract

We introduce Nevanlinna classes of holomorphic functions associated to a closed set on the boundary of the unit disc in the complex plane and we get Blaschke type theorems relative to these classes by use of several complex variables methods. This gives alternative proofs of some results of Favorov \& Golinskii, useful, in particular, for the study of eigenvalues of non self adjoint Schr{\"o}dinger operators.