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Jussi Behrndt & Seppo Hassi 
Boundary Value Problems, Weyl Functions, and Differential Operators 

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Cover of Jussi Behrndt & Seppo Hassi: Boundary Value Problems, Weyl Functions, and Differential Operators (PDF)



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.


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Table of Content

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.
Language English ● Format PDF ● Pages 772 ● ISBN 9783030367145 ● File size 9.1 MB ● Age 02-99 years ● Publisher Springer International Publishing ● City Cham ● Country CH ● Published 2020 ● Downloadable 24 months ● Currency EUR ● ID 7339520 ● Copy protection Adobe DRM
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