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A characterization of semibounded selfadjoint operators |
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| Authors: | Seppo Hassi Michael Kaltenbä ck Henk de Snoo |
| Affiliation: | Department of Statistics University of Helsinki PL 54, 00014 Helsinki Finland ; Institut für Analysis, Technische Mathematik und Versicherungsmathematik Technische Universität Wien Wiedner Hauptstrasse 8-10/114 A-1040 Wien Österreich ; Department of Mathematics University of Groningen Postbus 800, 9700 AV Groningen Nederland |
| Abstract: | For a class of closed symmetric operators  with defect numbers  it is possible to define a generalization of the Friedrichs extension, which coincides with the usual Friedrichs extension when  is semibounded. In this paper we provide an operator-theoretic interpretation of this class of symmetric operators. Moreover, we prove that a selfadjoint operator  is semibounded if and only if each one-dimensional restriction of  has a generalized Friedrichs extension. |
| Keywords: | Symmetric operator selfadjoint extension Friedrichs extension $Q$-function Nevanlinna function |
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