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Linear Fractional Transformations of Nevanlinna Functions Associated with a Nonnegative Operator |
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| Authors: | Jussi Behrndt Seppo Hassi Henk de Snoo Rudi Wietsma Henrik Winkler |
| Institution: | 1. Institut für Numerische Mathematik, Technische Universit?t Graz, Steyrergasse 30, 8010, Graz, Austria 2. Department of Mathematics and Statistics, University of Vaasa, P.O. Box 700, 65101, Vaasa, Finland 3. Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, P.O. Box 407, 9700 AK, Groningen, The Netherlands 4. Institut für Mathematik, Technische Universit?t Ilmenau, Curiebau, Weimarer Str. 25, 98693, Ilmenau, Germany |
| Abstract: | 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 ${(-\infty, a)\,\cup\, (a, 0)}$ . 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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