- 98-77 F. Gesztesy, N. J. Kalton, K. A. Makarov, and E. Tsekanovskii
- Some Applications of Operator-Valued Herglotz Functions
Feb 21, 98
(auto. generated ps),
of related papers
Abstract. We consider operator-valued Herglotz functions and their applications to
self-adjoint perturbations of self-adjoint operators and self-adjoint
extensions of densely defined closed symmetric operators. Our applications
include model operators for both situations, linear fractional
transformations for Herglotz operators, results on Friedrichs and Krein
extensions, and realization theorems for classes of Herglotz operators.
Moreover, we study the concrete case of Schr\"odinger operators on a
half-line and provide two illustrations of Livsic's result  on
quasi-hermitian extensions in the special case of densely defined symmetric
operators with deficiency indices (1,1).