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 (−∞, 0) and all those Nevanlinna functions that have one negative pole a and are injective on (−∞,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.