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oapen-20.500.12657-231022024-03-22T19:23:38Z Boundary Value Problems, Weyl Functions, and Differential Operators Behrndt, Jussi Hassi, Seppo de Snoo, Henk Mathematics Operator theory Differential equations 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 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. 2020-03-18 13:36:15 2020-04-01T09:03:40Z 2020-04-01T09:03:40Z 2020 book 1007056 http://library.oapen.org/handle/20.500.12657/23102 eng Monographs in Mathematics application/pdf n/a 1007056.pdf https://www.springer.com/9783030367145 Springer Nature 10.1007/978-3-030-36714-5 10.1007/978-3-030-36714-5 6c6992af-b843-4f46-859c-f6e9998e40d5 772 Cham open access
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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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