Boundary Value Problems, Weyl Functions, and Differential Operators: 108 (Monographs in Mathematics, 108) - Hardcover

Behrndt, Jussi; Hassi, Seppo; De Snoo, Henk

Hardcover

ISBN 10: 3030367134 ISBN 13: 9783030367138

Publisher: Birkhäuser, 2020

Synopsis

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.

About this title

From the Back Cover

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.

Edition details

• Publisher: Birkhäuser
• Publication date: 2020
• Language: English
• ISBN 10: 3030367134
• ISBN 13: 9783030367138
• Binding: Hardcover
• Edition number: 1
• Number of pages: 781