On Some Analytic Operator Functions in the Theory of Hermitian Operators

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On Some Analytic Operator Functions in the Theory of Hermitian Operators Perch Melik-Adamyan

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.

DOI: https://armjmath.sci.am/index.php/ajm/article/view/92 Armenian Journal of Mathematics, 5(2) 75-97

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Keywords

Hermitian operator, maximal extension, resolvent, characteristic function, Weylfunction, von Neumann’s formulas

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