About generalized zeros of non-regular generalized Nevanlinna functions. (Q1811179)

The paper first extends the definition of generalized zeros to those operator-valued Nevanlinna functions that are not regular, then points out the differences between this and the regular case, and then proves the existence of a rational function \(B(z)\), given a singular generalized Nevanlinna function \(Q\in N_\gamma\) such that \(B\) collects all generalized zeros and poles not of positive type and such that the function \(B(\overline z)^*Q(z)B(z)\) belongs to the Nevanlinna class \(N_0\).