Weyl function and spectral properties of self-adjoint extensions

By J. Brasche, M. Malamud, H. Neidhardt. 2002

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A description of all self-adjoint extensions of the Laplacian and Kreĭn-type resolvent formulas on non-smooth domains (2009, background): “84], [6], [7], [9], [10], [16], [17], [23], [24], [25], [26], [29], [30], [32], [33], [34], [35], [36], [38], [39], [40], [41], [51], [52], [53], [58], [59], [60, Ch.”
Boundary pairs associated with quadratic forms (2012, background): “3], [74], [24], [22], going back to ideas already contained in [83] and [41]).”
Boundary relations and generalized resolvents of symmetric operators (2006, unknown): “one obtains a boundary triplet ΠA = {C, Γ0, Γ1} for A ∗ = S ∗ 1 , and the corresponding Weyl function is given by M (λ )= ±i, λ ∈ C±; cf. [ 10 ].”
Boundary Value Problems, Weyl Functions, and Differential Operators (2020, background): “This description was extended in [155] to the abstract setting of boundary triplets and Weyl functions in the case where the underlying symmetric operator is densely defined and simple (on R).”
SPECTRA OF SELF-ADJOINT EXTENSIONS AND APPLICATIONS TO SOLVABLE SCHRÖDINGER OPERATORS (2006, background): “Some of our results are close to that obtained in [24] for simple operators, but are expressed in d ifferent terms.”