Armenian Journal of Mathematics, 5(2)
2014; 75–97
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On Some Analytic Operator Functions in the Theory of Hermitian Operators

Perch Melik-Adamyan*

Received: 2024-12-19 · Published: 2014-01-08

© 2014 The Author(s) and the original publisher.

CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Original title
On Some Analytic Operator Functions in the Theory of Hermitian Operators
Author
Perch Melik-Adamyan
Source journal
Armenian Journal of Mathematics, 5(2)
Published
2014-01-08
Licence
Creative Commons Attribution 4.0 International
Original
https://armjmath.sci.am/index.php/ajm/article/view/92

Abstract

A densely defined Hermitian operatorA0with equal defect numbers is con-sidered. Presentable by means of resolvents of a certain maximal dissipative oraccumulative extensions ofA0, bounded linear operators acting from some defectsubspaceNγto arbitrary otherNλare investigated. With their aid are discussedcharacteristic and Weyl functions. A family of Weyl functions is described, as-sociated with a given self-adjoint extension ofA0. The specific property of Weylfunction’s factors enabled to obtain a modified formulas of von Neumann. Interms of characteristic and Weyl functions of suitably chosen extensions the re-solvent of Weyl function is presented explicitly.
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