Boundary Value Problems, Weyl Functions, and Differential Operators

• Format: eBook
• Language: English
• Published: Cham Springer Nature 2020
• Series: Monographs in Mathematics
• Subjects: Differential equations; Mathematics; Operator theory; Partial differential equations; System theory; thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general::GPF Information theory::GPFC Cybernetics and systems theory; thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKF Functional analysis and transforms; thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKJ Differential calculus and equations
• Online Access: Open Access: DOAB: description of the publication; Open Access: DOAB, download 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.