About Generalized Zeros of Non-Regular Generalized Nevanlinna Functions

The definition of a generalized zero is extended to those operator valued generalized Nevanlinna functions Q(element of)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(element of)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(z )*Q(z)B(z)belongs to the Nevanlinna class N_0(H).