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On a formula of the generalized resolvents of a nondensely defined Hermitian operator
The Weyl function and the prohibited lineal, corresponding to a given space of boundary values of a nondensely defined Hermitian operator, are introduced and investigated. The prohibited lineal is
Boundary relations and their Weyl families
The concepts of boundary relations and the corresponding Weyl families are introduced. Let S be a closed symmetric linear operator or, more generally, a closed symmetric relation in a Hilbert space
Boundary relations and generalized resolvents of symmetric operators
The Kreĭn-Naĭmark formula provides a parametrization of all selfadjoint exit space extensions of a (not necessarily densely defined) symmetric operator in terms of maximal dissipative (in ℂ+)
Spectral theory of semibounded Sturm–Liouville operators with local interactions on a discrete set
We study the Hamiltonians HX,α,q with δ-type point interactions at the centers xk on the positive half line in terms of energy forms. We establish analogs of some classical results on operators
Scattering matrices and Weyl functions
For a scattering system {AΘ, A0} consisting of self‐adjoint extensions AΘ and A0 of a symmetric operator A with finite deficiency indices, the scattering matrix {SΘ(λ)} and a spectral shift function
Weyl function and spectral properties of self-adjoint extensions
We characterize the spectra of self-adjoint extensions of a symmetric operator with equal deficiency indices in terms of boundary values of their Weyl functions. A complete description is obtained