Abstract The Dirichlet-to-Neumann map associated to an elliptic partial differential equation
becomes multivalued when the underlying Dirichlet problem is not uniquely solvable. The …

In this paper, the spectral and scattering properties of a family of self-adjoint Dirac operators
in L^ 2 (Ω; C^ 4) L 2 (Ω; C 4), where Ω ⊂ R^ 3 Ω⊂ R 3 is either a bounded or an unbounded …

A general representation formula for the scattering matrix of a scattering system consisting of
two self-adjoint operators in terms of an abstract operator valued Titchmarsh–Weyl m …

The spectrum of a selfadjoint second order elliptic differential operator in L 2 (R n) is
described in terms of the limiting behavior of Dirichlet-to-Neumann maps, which arise in a …

Let $\dot {A} $ be a densely defined, closed, symmetric operator in the complex, separable
Hilbert space $\mathcal {H} $ with equal deficiency indices and denote by $\mathcal {N} …

The question of self-adjoint realizations of sign-indefinite second-order differential operators
is discussed in terms of a model problem. Operators of the type are generalized to finite, not …

After reviewing basic facts on bounded operator-valued Nevanlinna–Herglotz functions, we
point out some of the highlights of Sergey Naboko's results in connection with nontangential …

Given a complex, separable Hilbert space H, we consider differential expressions of the type
τ=−(d 2/dx 2) IH+ V (x), with x∈(x 0,∞) for some x 0∈ ℝ, or x∈ ℝ (assuming the limit-point …

This thesis is devoted to the spectral theory of differential operators on metric graphs and of
indefinite differential operators on bounded domains. It consists of two parts. In the first part …

For a second order formally symmetric elliptic differential expression we show that the
knowledge of the Dirichlet-to-Neumann map or Robin-to-Dirichlet map for suitably many …