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

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 in...

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Bibliographic Details
Main Author: Perch Melik-Adamyan
Format: Article
Language:English
Published: Republic of Armenia National Academy of Sciences 2016-06-01
Series:Armenian Journal of Mathematics
Online Access:http://test.armjmath.sci.am/index.php/ajm/article/view/120
Description
Summary: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.
ISSN:1829-1163