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

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

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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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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://armjmath.sci.am/index.php/ajm/article/view/120
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spelling doaj-77926abcfa434bb0b738e8302d91c44b2020-11-25T01:42:40ZengRepublic of Armenia National Academy of SciencesArmenian Journal of Mathematics1829-11632016-06-0181On Nagy-Foias Characteristic Function in Extensions Theory of Hermitian OperatorsPerch Melik-Adamyan0Institute of Mechanics of NAS Armenia 24b Marshal Baghramian Ave. Yerevan 0019, Armenia 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. http://armjmath.sci.am/index.php/ajm/article/view/120
collection DOAJ
language English
format Article
sources DOAJ
author Perch Melik-Adamyan
spellingShingle Perch Melik-Adamyan
On Nagy-Foias Characteristic Function in Extensions Theory of Hermitian Operators
Armenian Journal of Mathematics
author_facet Perch Melik-Adamyan
author_sort Perch Melik-Adamyan
title On Nagy-Foias Characteristic Function in Extensions Theory of Hermitian Operators
title_short On Nagy-Foias Characteristic Function in Extensions Theory of Hermitian Operators
title_full On Nagy-Foias Characteristic Function in Extensions Theory of Hermitian Operators
title_fullStr On Nagy-Foias Characteristic Function in Extensions Theory of Hermitian Operators
title_full_unstemmed On Nagy-Foias Characteristic Function in Extensions Theory of Hermitian Operators
title_sort on nagy-foias characteristic function in extensions theory of hermitian operators
publisher Republic of Armenia National Academy of Sciences
series Armenian Journal of Mathematics
issn 1829-1163
publishDate 2016-06-01
description 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.
url http://armjmath.sci.am/index.php/ajm/article/view/120
work_keys_str_mv AT perchmelikadamyan onnagyfoiascharacteristicfunctioninextensionstheoryofhermitianoperators
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