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Beschreibung
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 Schrödinger 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.
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.
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 Schrödinger 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.
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.
Zusammenfassung
Self-contained and written in an accessible style
Provides an overview of the theory of boundary triplet techniques
Inhaltsverzeichnis
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 Carathéodory functions.- The integral representation of Nevanlinna functions.
Details
Erscheinungsjahr: | 2020 |
---|---|
Fachbereich: | Analysis |
Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
Rubrik: | Naturwissenschaften & Technik |
Medium: | Buch |
Inhalt: |
ix
772 S. 1 s/w Illustr. 772 p. 1 illus. |
ISBN-13: | 9783030367138 |
ISBN-10: | 3030367134 |
Sprache: | Englisch |
Einband: | Gebunden |
Autor: |
Behrndt, Jussi
de Snoo, Henk Hassi, Seppo |
Auflage: | 1st edition 2020 |
Hersteller: |
Springer International Publishing
Springer International Publishing AG |
Verantwortliche Person für die EU: | Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com |
Maße: | 241 x 160 x 48 mm |
Von/Mit: | Jussi Behrndt (u. a.) |
Erscheinungsdatum: | 04.01.2020 |
Gewicht: | 1,326 kg |
Zusammenfassung
Self-contained and written in an accessible style
Provides an overview of the theory of boundary triplet techniques
Inhaltsverzeichnis
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 Carathéodory functions.- The integral representation of Nevanlinna functions.
Details
Erscheinungsjahr: | 2020 |
---|---|
Fachbereich: | Analysis |
Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
Rubrik: | Naturwissenschaften & Technik |
Medium: | Buch |
Inhalt: |
ix
772 S. 1 s/w Illustr. 772 p. 1 illus. |
ISBN-13: | 9783030367138 |
ISBN-10: | 3030367134 |
Sprache: | Englisch |
Einband: | Gebunden |
Autor: |
Behrndt, Jussi
de Snoo, Henk Hassi, Seppo |
Auflage: | 1st edition 2020 |
Hersteller: |
Springer International Publishing
Springer International Publishing AG |
Verantwortliche Person für die EU: | Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com |
Maße: | 241 x 160 x 48 mm |
Von/Mit: | Jussi Behrndt (u. a.) |
Erscheinungsdatum: | 04.01.2020 |
Gewicht: | 1,326 kg |
Sicherheitshinweis