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On Representations of Matrix Valued Nevanlinna Functions by u ‐ Resolvents

We show that every matrix valued generalized Nevanlinna function can be represented as a u‐resolvent of a certain selfadjoint relation acting in a Pontryagin space. The negative index of this Pontryagin space may be larger than the number of negative squares of the given function. The minimal index of negative squares which is needed to obtain such a representation is determined. In the case of scalar functions, the results presented give rise to some new classes of generalized Nevanlinna functions.