Linear fractional transformations of Nevanlinna functions associated with a nonnegative operator

In the present paper a subclass of scalar Nevanlinna functions is studied, which coincides with the class of Weyl functions associated to a nonnegative symmetric operator of defect one in a Hilbert space. This class consists of all Nevanlinna functions that are holomorphic on (1; 0) and all those Nevanlinna functions that have one negative pole a and are injective on (1; a)[(a; 0). These functions are characterized via integral representations and special attention is paid to linear fractional transformations which arise in extension and spectral problems of symmetric and selfadjoint operators.


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