About Generalized Zeros of Non-Regular Generalized Nevanlinna Functions

Abstract.

The definition of a generalized zero is extended to those operator valued generalized Nevanlinna functions $Q\in\mathcal{N_{K}(H)}$ which are not regular. Differences to the regular case are pointed out and it is shown that also for a singular generalized Nevanlinna function $Q\in\mathcal{N_{K}(H)}$ there exists a rational function B(z) which collects the generalized poles and zeros that are not of positive type, such that the function ¶¶B( $ \overline{z} $ )*Q(z)B(z)¶¶belongs to the Nevanlinna class $\mathcal{N}_{0}{\mathcal(H)}$ .