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 is an 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 E X (R) 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) over bar)*Q(z)B(z) belongs to the Nevanlinna class No(H).