Linear fractional transformations of Nevanlinna functions associated with a nonnegative operator

Behrndt, Jussi GND; Hassi, Seppo GND; Snoo, Henk de; Wietsma, Rudi; Winkler, Henrik GND

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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Behrndt Univ.-Prof. Dr., J., Hassi Prof. Dr., S., Snoo Prof. Dr., H. de, Wietsma M.sc., R., Winkler Priv.-Doz. Dr. rer. nat. habil., H., 2011. Linear fractional transformations of Nevanlinna functions associated with a nonnegative operator. Preprint /  Technische Universität Ilmenau, Institut für Mathematik, Preprint /  Technische Universität Ilmenau, Institut für Mathematik 11–18.
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