# On Some Analytic Operator Functions in the Theory of Hermitian Operators

## Abstract

A densely defined Hermitian operator $A_0$ with equal defect numbers is considered. Presentable by means of resolvents of a certain maximal dissipative or accumulative extensions of $A_0$, bounded linear operators acting from some defect subspace $\mfn_\gamma$ to arbitrary other $\mfn_\lambda$ are investigated. With their aid are discussed characteristic and Weyl functions. A family of Weyl functions is described, associated with a given self-adjoint extension of $A_0$. The specific property of Weyl function's factors enabled to obtain a modified formulas of von Neumann. In terms of characteristic and Weyl functions of suitably chosen extensions the resolvent of Weyl function is presented explicitly.

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## Published

2014-01-08

## How to Cite

*Armenian Journal of Mathematics*,

*5*(2), 75-97. Retrieved from http://armjmath.sci.am/index.php/ajm/article/view/92

## Issue

## Section

Articles