A factorization of regular generalized Nevanlinna functions (Q698275)

A regular operator valued generalized Nevanlinna function \(Q\) with negative index \(k\) was studied \((Q\in{\mathcal N} ({\mathcal H})\), \({\mathcal N}({\mathcal H})\) is the Nevanlinna class, \({\mathcal H}\) is the Hilbert space). A corresponding factorization for regular operator functions \(Q\) was carried out. The case of not orthogonal and of orthogonal root vectors was discussed. It was shown that there exists a rational function \(B(z)\), which collects the generalized poles and zeros of \(Q\) that are not of positive type such that the functions \(B (\overline z)^* Q(z)B(z)\) belong to the Nevanlinna class \({\mathcal N}_0 ({\mathcal H})\).