On Some Analytic Operator Functions in the Theory of Hermitian Operators

On Some Analytic Operator Functions in the Theory of Hermitian Operators

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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...

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Main Author: Perch Melik-Adamyan
Format: Article
Language:English
Published: Republic of Armenia National Academy of Sciences 2014-01-01
Series:Armenian Journal of Mathematics
Online Access:http://armjmath.sci.am/index.php/ajm/article/view/92
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spelling doaj-1d9cc4bb1d5d4fc9bc9e0fd3c4e9ae6d2020-11-24T23:38:06ZengRepublic of Armenia National Academy of SciencesArmenian Journal of Mathematics1829-11632014-01-0152On Some Analytic Operator Functions in the Theory of Hermitian OperatorsPerch Melik-Adamyan 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. http://armjmath.sci.am/index.php/ajm/article/view/92
collection DOAJ
language English
format Article
sources DOAJ
author Perch Melik-Adamyan
spellingShingle Perch Melik-Adamyan
On Some Analytic Operator Functions in the Theory of Hermitian Operators
Armenian Journal of Mathematics
author_facet Perch Melik-Adamyan
author_sort Perch Melik-Adamyan
title On Some Analytic Operator Functions in the Theory of Hermitian Operators
title_short On Some Analytic Operator Functions in the Theory of Hermitian Operators
title_full On Some Analytic Operator Functions in the Theory of Hermitian Operators
title_fullStr On Some Analytic Operator Functions in the Theory of Hermitian Operators
title_full_unstemmed On Some Analytic Operator Functions in the Theory of Hermitian Operators
title_sort on some analytic operator functions in the theory of hermitian operators
publisher Republic of Armenia National Academy of Sciences
series Armenian Journal of Mathematics
issn 1829-1163
publishDate 2014-01-01
description 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.
url http://armjmath.sci.am/index.php/ajm/article/view/92
work_keys_str_mv AT perchmelikadamyan onsomeanalyticoperatorfunctionsinthetheoryofhermitianoperators
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