Some Applications of Operator-Valued Herglotz Functions

@article{Gesztesy2001SomeAO,
  title={Some Applications of Operator-Valued Herglotz Functions},
  author={Fritz Gesztesy and Nigel J. Kalton and K. A. Makarov and Eduard Tsekanovskii},
  journal={arXiv: Functional Analysis},
  year={2001},
  pages={271-321}
}
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 Schrodinger operators on a half… 
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