Extensions of symmetric operators I: The inner characteristic function case

Given a symmetric linear transformation on a Hilbert space, a natural problem to consider is the characterization of its set of symmetric extensions. This problem is equivalent to the study of the partial isometric extensions of a fixed partial isometry. We provide a new function theoretic character...
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Autor*in:	Martin R.T.W. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2015

Schlagwörter:	symmetric operators partial isometries self-adjoint and unitary extensions reproducing kernel Hilbert spaces of analytic functions Hardy and deBranges Rovnyak spaces Livšic characteristic function

Übergeordnetes Werk:	In: Concrete Operators - De Gruyter, 2015, 2(2015), 1
Übergeordnetes Werk:	volume:2 ; year:2015 ; number:1

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1515/conop-2015-0004

Katalog-ID:	DOAJ025862286

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520			\|a Given a symmetric linear transformation on a Hilbert space, a natural problem to consider is the characterization of its set of symmetric extensions. This problem is equivalent to the study of the partial isometric extensions of a fixed partial isometry. We provide a new function theoretic characterization of the set of all self-adjoint extensions of any symmetric linear transformation B with finite equal indices and inner Livšic characteristic function θB by constructing a bijection between the quotient of this set by a certain natural equivalence relation and the set of all contractive analytic functions φ which are greater or equal to θB.
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650		4	\|a Livšic characteristic function
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callnumber-first	Q - Science
author	Martin R.T.W.
spellingShingle	Martin R.T.W. misc QA1-939 misc symmetric operators misc partial isometries misc self-adjoint and unitary extensions misc reproducing kernel Hilbert spaces of analytic functions misc Hardy and deBranges Rovnyak spaces misc Livšic characteristic function misc Mathematics Extensions of symmetric operators I: The inner characteristic function case
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topic_title	QA1-939 Extensions of symmetric operators I: The inner characteristic function case symmetric operators partial isometries self-adjoint and unitary extensions reproducing kernel Hilbert spaces of analytic functions Hardy and deBranges Rovnyak spaces Livšic characteristic function
topic	misc QA1-939 misc symmetric operators misc partial isometries misc self-adjoint and unitary extensions misc reproducing kernel Hilbert spaces of analytic functions misc Hardy and deBranges Rovnyak spaces misc Livšic characteristic function misc Mathematics
topic_unstemmed	misc QA1-939 misc symmetric operators misc partial isometries misc self-adjoint and unitary extensions misc reproducing kernel Hilbert spaces of analytic functions misc Hardy and deBranges Rovnyak spaces misc Livšic characteristic function misc Mathematics
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title	Extensions of symmetric operators I: The inner characteristic function case
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title_full	Extensions of symmetric operators I: The inner characteristic function case
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title_sort	extensions of symmetric operators i: the inner characteristic function case
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title_auth	Extensions of symmetric operators I: The inner characteristic function case
abstract	Given a symmetric linear transformation on a Hilbert space, a natural problem to consider is the characterization of its set of symmetric extensions. This problem is equivalent to the study of the partial isometric extensions of a fixed partial isometry. We provide a new function theoretic characterization of the set of all self-adjoint extensions of any symmetric linear transformation B with finite equal indices and inner Livšic characteristic function θB by constructing a bijection between the quotient of this set by a certain natural equivalence relation and the set of all contractive analytic functions φ which are greater or equal to θB.
abstractGer	Given a symmetric linear transformation on a Hilbert space, a natural problem to consider is the characterization of its set of symmetric extensions. This problem is equivalent to the study of the partial isometric extensions of a fixed partial isometry. We provide a new function theoretic characterization of the set of all self-adjoint extensions of any symmetric linear transformation B with finite equal indices and inner Livšic characteristic function θB by constructing a bijection between the quotient of this set by a certain natural equivalence relation and the set of all contractive analytic functions φ which are greater or equal to θB.
abstract_unstemmed	Given a symmetric linear transformation on a Hilbert space, a natural problem to consider is the characterization of its set of symmetric extensions. This problem is equivalent to the study of the partial isometric extensions of a fixed partial isometry. We provide a new function theoretic characterization of the set of all self-adjoint extensions of any symmetric linear transformation B with finite equal indices and inner Livšic characteristic function θB by constructing a bijection between the quotient of this set by a certain natural equivalence relation and the set of all contractive analytic functions φ which are greater or equal to θB.
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title_short	Extensions of symmetric operators I: The inner characteristic function case
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