Titlebook: Boundary Value Problems, Weyl Functions, and Differential Operators; Jussi Behrndt,Seppo Hassi,Henk de Snoo Book‘‘‘‘‘‘‘‘ 2020 The Editor(s

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https://doi.org/10.1007/978-3-030-37767-0In this monograph the theory of boundary triplets and their Weyl functions is developed and applied to the analysis of boundary value problems for differential equations and general operators in Hilbert spaces.

Acumen

Elizabeth I and the Dilemma of LoyaltyA linear relation from one Hilbert space to another Hilbert space is a linear subspace of the product of these spaces. In this chapter some material about such linear relations is presented and it is shown how linear operators, whether densely defined or not, fit in this context.

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Ischemia

Elizabeth I and the Dilemma of LoyaltyIn this chapter the spectrum of a self-adjoint operator or relation will be completely characterized in terms of the analytic behavior and the limit properties of the Weyl function.

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Spectral theory for Lp-operators,The classes of Weyl functions and more generally of Nevanlinna functions will be studied from the point of view of reproducing kernel Hilbert spaces.

Choreography

LP-Structure in Real Banach SpacesSemibounded relations in a Hilbert space automatically have equal defect numbers, so that there are always self-adjoint extensions. In this chapter the semibounded self-adjoint extensions of a semibounded relation will be investigated.

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Energy Preserving Boundary ConditionsSecond-order Sturm-Liouville differential expressions generate self-adjoint differential operators in weighted.-spaces on an interval (.,.).

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Energy Preserving Boundary ConditionsFor the multi-dimensional Schr?dinger operator -?+V with a bounded real potential V on a bounded domain . with a C2-smooth boundary a boundary triplet and a Weyl function will be constructed.

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