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Boundary value problems, Weyl functi...

Behrndt, Jussi.

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Boundary value problems, Weyl functions, and differential operators

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Boundary value problems, Weyl functions, and differential operators/ by Jussi Behrndt, Seppo Hassi, Henk de Snoo.
作者:	Behrndt, Jussi.
其他作者:	Hassi, Seppo.
出版者:	Cham :Springer International Publishing : : 2020.,
面頁冊數:	ix, 772 p. :ill., digital ;24 cm.
內容註:	Linear relations -- Boundary triplets and Weyl functions -- Spectra and Weyl functions -- Operator models -- Nonnegative selfadjoint extensions -- Sturm-Liouville operators -- Canonical systems -- Schrodinger operators -- Sums of closed subspaces in a Hilbert space -- Factorization of bounded linear operators -- Integral representations of Caratheodory functions -- The integral representation of Nevanlinna functions.
Contained By:	Springer Nature eBook
標題:	Boundary value problems. -
電子資源:	https://doi.org/10.1007/978-3-030-36714-5
ISBN:	9783030367145

Boundary value problems, Weyl functions, and differential operators
Behrndt, Jussi.

Boundary value problems, Weyl functions, and differential operators[electronic resource] /by Jussi Behrndt, Seppo Hassi, Henk de Snoo. - Cham :Springer International Publishing :2020. - ix, 772 p. :ill., digital ;24 cm. - Monographs in mathematics,v.1081017-0480 ;. - Monographs in mathematics ;v.108..

Linear relations -- Boundary triplets and Weyl functions -- Spectra and Weyl functions -- Operator models -- Nonnegative selfadjoint extensions -- Sturm-Liouville operators -- Canonical systems -- Schrodinger operators -- Sums of closed subspaces in a Hilbert space -- Factorization of bounded linear operators -- Integral representations of Caratheodory functions -- The integral representation of Nevanlinna functions.

Open access.

This open access book presents a comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions. It includes self-contained treatments of the extension theory of symmetric operators and relations, spectral characterizations of selfadjoint operators in terms of the analytic properties of Weyl functions, form methods for semibounded operators, and functional analytic models for reproducing kernel Hilbert spaces. Further, it illustrates these abstract methods for various applications, including Sturm-Liouville operators, canonical systems of differential equations, and multidimensional Schrodinger operators, where the abstract Weyl function appears as either the classical Titchmarsh-Weyl coefficient or the Dirichlet-to-Neumann map. The book is a valuable reference text for researchers in the areas of differential equations, functional analysis, mathematical physics, and system theory. Moreover, thanks to its detailed exposition of the theory, it is also accessible and useful for advanced students and researchers in other branches of natural sciences and engineering.

ISBN: 9783030367145

Standard No.: 10.1007/978-3-030-36714-5doiSubjects--Topical Terms:

527599
Boundary value problems.

LC Class. No.: QA379 / .B44 2020

Dewey Class. No.: 515.35

Boundary value problems, Weyl functions, and differential operators
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505 0 $a Linear relations -- Boundary triplets and Weyl functions -- Spectra and Weyl functions -- Operator models -- Nonnegative selfadjoint extensions -- Sturm-Liouville operators -- Canonical systems -- Schrodinger operators -- Sums of closed subspaces in a Hilbert space -- Factorization of bounded linear operators -- Integral representations of Caratheodory functions -- The integral representation of Nevanlinna functions.
506 $a Open access.
520 $a This open access book presents a comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions. It includes self-contained treatments of the extension theory of symmetric operators and relations, spectral characterizations of selfadjoint operators in terms of the analytic properties of Weyl functions, form methods for semibounded operators, and functional analytic models for reproducing kernel Hilbert spaces. Further, it illustrates these abstract methods for various applications, including Sturm-Liouville operators, canonical systems of differential equations, and multidimensional Schrodinger operators, where the abstract Weyl function appears as either the classical Titchmarsh-Weyl coefficient or the Dirichlet-to-Neumann map. The book is a valuable reference text for researchers in the areas of differential equations, functional analysis, mathematical physics, and system theory. Moreover, thanks to its detailed exposition of the theory, it is also accessible and useful for advanced students and researchers in other branches of natural sciences and engineering.
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