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.
|Number of pages||12|
|Journal||Proceedings of the american mathematical society|
|Publication status||Published - Sep-1997|
- Nevanlinna function
- Friedrichs extension
- selfadjoint extension
- symmetric operator