On Some Analytic Operator Functions in the Theory of Hermitian Operators
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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| Format: | Article |
| Language: | English |
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Republic of Armenia National Academy of Sciences
2014-01-01
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| Series: | Armenian Journal of Mathematics |
| Online Access: | http://www.armjmath.sci.am/index.php/ajm/article/view/92 |
| Summary: | 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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| ISSN: | 1829-1163 |