On Nagy-Foias Characteristic Function in Extensions Theory of Hermitian Operators

Authors

  • Perch Melik-Adamyan Institute of Mechanics of NAS Armenia 24b Marshal Baghramian Ave. Yerevan 0019, Armenia

Abstract

For a densely defined in a Hilbert space closed Hermitian operator with infinite defect numbers its maximal extensions are discussed. The Nagy-Foias characteristic function of an arbitrary maximal dissipative extension is derived. Mutually complementary classes of such extensions, referred to as inherited and acquired are introduced, and the peculiarity of characteristic function, as determining the class of extensions it corresponds to, is noted. In the setting of Calkin's abstract boundary conditions theory abstract analogs of Nagy-Foias and Weyl functions are presented in similar manner, as operator functions involved in boundary operators, describing the class of inherited extensions. Existence and analyticity of these functions are proved.

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Published

2016-06-07

How to Cite

Melik-Adamyan, P. (2016). On Nagy-Foias Characteristic Function in Extensions Theory of Hermitian Operators. Armenian Journal of Mathematics, 8(1), 1-24. Retrieved from http://armjmath.sci.am/index.php/ajm/article/view/120

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