Boundary Value Problems, Weyl Functions, and Differential Operators

• Main Author: Behrndt, Jussi (auth)
• Other Authors: Hassi, Seppo (auth), de Snoo, Henk (auth)
• Format: Electronic Book Chapter
• Language: English
• Published: Cham Springer Nature 2020
• Series: Monographs in Mathematics
• Subjects: Cybernetics & systems theory; Functional analysis & transforms; Differential calculus & equations; Mathematics; Operator theory; Differential equations; Partial differential equations; System theory
• Online Access: OAPEN Library: download the publication; OAPEN Library: description of the publication

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.