Abstract
For a class of closed symmetric operators S with defect numbers (1, 1) it is possible to define a generalization of the Friedrichs extension, which coincides with the usual Friedrichs extension when S is semibounded. In this paper we provide an operator-theoretic interpretation of this class of symmetric operators. Moreover, we prove that a selfadjoint operator A is semibounded if and only if each one-dimensional restriction of A has a generalized Friedrichs extension.
Original language | English |
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Pages (from-to) | 2681-2692 |
Number of pages | 12 |
Journal | Proceedings of the american mathematical society |
Volume | 125 |
Issue number | 9 |
Publication status | Published - Sept-1997 |
Keywords
- Nevanlinna function
- Q-function
- Friedrichs extension
- selfadjoint extension
- symmetric operator