Armenian Journal of Mathematics

On Some Analytic Operator Functions in the Theory of Hermitian Operators

Melik-Adamyan, Perch (2013) On Some Analytic Operator Functions in the Theory of Hermitian Operators. Armenian Journal of Mathematics, 5 (2). pp. 75-97. ISSN 1829-1163

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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.

Item Type:Article
Subjects:47-xx Operator theory
ID Code:570
Deposited By:Unnamed user with email maperch@gmail.com
Deposited On:08 Jan 2014 11:23
Last Modified:10 Jan 2014 13:41

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