Boundary Value Problems, Weyl Functions, and Differential Operators

; Seppo Hassi ; Henk de Snoo

Serie: Monographs in Mathematics 108

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. Les mer
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Paperback
Legg i
Vår pris: 759,-

(Paperback) Fri frakt!
Leveringstid: Sendes innen 21 dager

Om boka

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 Schroedinger 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.

Fakta

Innholdsfortegnelse

Linear relations.- Boundary triplets and Weyl functions.- Spectra and Weyl functions.- Operator models.- Nonnegative selfadjoint extensions.- Sturm-Liouville operators.- Canonical systems.- Schr odinger 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.