On Some Analytic Operator Functions in the Theory of Hermitian Operators

Authors

  • Perch Melik-Adamyan

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

Melik-Adamyan, P. (2014). On Some Analytic Operator Functions in the Theory of Hermitian Operators. Armenian Journal of Mathematics, 5(2), 75-97. Retrieved from http://armjmath.sci.am/index.php/ajm/article/view/92

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