相关论文: Unitary equivalence of proper extensions of a symm…

It is a classical result that the Weyl function of a simple symmetric operator in a Hilbert space determines a boundary triple uniquely up to unitary equivalence. We generalize this result to a simple symmetric operator in a Pontryagin…

The Weyl family of a dual pair $A\subseteq B^c$ of operators in a Krein space determines a minimal boundary triple uniquely up to similarity; if $A=B$, a necessary and sufficient condition in order that the similarity should be unitary is…

The spectral problem for self-adjoint extensions is studied using the machinery of boundary triplets. For a class of symmetric operators having Weyl functions of a special type we calculate explicitly the spectral projections in the form of…

Given the symmetric operator $A_N$ obtained by restricting the self-adjoint operator $A$ to $N$, a linear dense set, closed with respect to the graph norm, we determine a convenient boundary triple for the adjoint $A_N^*$ and the…

With a closed symmetric operator $A$ in a Hilbert space ${\mathfrak H}$ a triple $\Pi=\{{\mathcal H},\Gamma_0,\Gamma_1\}$ of a Hilbert space ${\mathcal H}$ and two abstract trace operators $\Gamma_0$ and $\Gamma_1$ from $A^*$ to ${\mathcal…

The classical Weyl-von Neumann theorem states that for any self-adjoint operator $A$ in a separable Hilbert space $\mathfrak H$ there exists a (non-unique) Hilbert-Schmidt operator $C = C^*$ such that the perturbed operator $A+C$ has purely…

Let $A$ be a densely defined symmetric operator with equal deficiency indices in a Hilbert space. We introduce the notion of a Weyl function $M(z)$ of $A$ corresponding to an ordinary boundary triplet of the operator $A^*$ and then…

We consider symmetric operators of the form $S := A\otimes I_{\mathfrak T} + I_{\mathfrak H} \otimes T$ where $A$ is symmetric and $T = T^*$ is (in general) unbounded. Such operators naturally arise in problems of simulating point contacts…

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 are determined by abstract boundary conditions and we…

In this note semibounded self-adjoint extensions of symmetric operators are investigated with the help of the abstract notion of quasi boundary triples and their Weyl functions. The main purpose is to provide new sufficient conditions on…

The spectral properties of non-self-adjoint extensions $A_{[B]}$ of a symmetric operator in a Hilbert space are studied with the help of ordinary and quasi boundary triples and the corresponding Weyl functions. These extensions are given in…

We extend the notion of generalized boundary triples and their Weyl functions from extension theory of symmetric operators to adjoint pairs of operators, and we provide criteria on the boundary parameters to induce closed operators with a…

We consider a class of self-adjoint extensions using the boundary triple technique. Assuming that the associated Weyl function has the special form $M(z)=\big(m(z)\Id-T\big) n(z)^{-1}$ with a bounded self-adjoint operator $T$ and scalar…

The notion of quasi boundary triples and their Weyl functions from extension theory of symmetric operators is extended to the general framework of adjoint pairs of operators under minimal conditions on the boundary maps. With the help of…

The abstract theory of boundary triples is applied to the classical Jacobi differential operator and its powers in order to obtain the Weyl $m$-function for several self-adjoint extensions with interesting boundary conditions: separated,…

The notion of quasi boundary triples and their Weyl functions is an abstract concept to treat spectral and boundary value problems for elliptic partial differential equations. In the present paper the abstract notion is further developed,…

We use the boundary triplet approach to extend the classical concept of perturbation determinants to a more general setup. In particular, we examine the concept of perturbation determinants to pairs of proper extensions of closed symmetric…

For a scattering system $\{A_\Theta,A_0\}$ consisting of selfadjoint extensions $A_\Theta$ and $A_0$ of a symmetric operator $A$ with finite deficiency indices, the scattering matrix $\{S_\gT(\gl)\}$ and a spectral shift function…

Based on the relationship of symmetric operators with Hermitian symmetric spaces, we introduce the notion of \emph{Weyl curve} for a symmetric operator $T$, which is the geometric abstraction and generalization of the well-known Weyl…

In this article we develop a systematic approach to treat Dirac operators $A_{\eta, \tau, \lambda}$ with singular electrostatic, Lorentz scalar, and anomalous magnetic interactions of strengths $\eta, \tau, \lambda \in \mathbb{R}$,…