A Hermitian operator A with gaps (α j, β j)(1⩽ j⩽ m⩽∞) is studied. The self-adjoint
extensions which put exactly kj<∞ eigenvalues into each gap (α j, β j), in particular (for kj= 0 …

This paper is dedicated to further development of the theory of generalized resolvents,
preresolvent, and resolvent matrices of a Hermitian operator A on a separable Hilbert space …

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 …

This open access book gives a systematic introduction into the spectral theory of differential
operators on metric graphs. Main focus is on the fundamental relations between the …

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 …

Abstract 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 …

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 …

Starting with an adjoint pair of operators, under suitable abstract versions of standard PDE
hypotheses, we consider the Weyl M-function of extensions of the operators. The extensions …

In this paper, we combine results on extensions of operators with recent results on the
relation between the M‐function and the spectrum, to examine the spectral behaviour of …

For a scattering system {A Θ, A 0} consisting of self-adjoint extensions A Θ and A 0 of a
symmetric operator A with finite deficiency indices, the scattering matrix {S Θ (λ)} and a …