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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 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.
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.
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