Related papers: Boundary relations and generalized resolvents of s…
Let $(\mathfrak{L},\Gamma)$ be an isometric boundary pair associated with a closed symmetric linear relation $T$ in a Krein space $\mathfrak{H}$. Let $M_\Gamma$ be the Weyl family corresponding to $(\mathfrak{L},\Gamma)$. We cope with two…
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…
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…
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…
New classes of generalized Nevanlinna functions, which under multiplication with an arbitrary fixed symmetric rational function remain generalized Nevanlinna functions, are introduced. Characterizations for these classes of functions are…
For the relations generated by pair of differential operator expressions one of which depends on the spectral parameter in the Nevanlinna manner we construct analogs of the generalized resolvents which are integro-differential operators.
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…
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,…
We study general (not necessarily Hamiltonian) first-order symmetric system $J y'-B(t)y=\D(t) f(t)$ on an interval $\cI=[a,b) $ with the regular endpoint $a$ and singular endpoint $b$. It is assumed that the deficiency indices $n_\pm(\Tmi)$…
It is known that the Weyl families corresponding to unitary boundary pairs $(\mathcal{H},\Gamma)$ belong to the class $\tilde{\mathcal{R}}(\mathcal{H})$ of Nevanlinna families. Here we extend the theorem to the case of essentially unitary…
For the relations generated by pair of differential operator expressions one of which depends on the spectral parameter in the Nevanlinna manner we construct analogs of the generalized resolvents which are integro-differential operators.…
The paper reports on a recent construction of M-functions and Krein resolvent formulas for general closed extensions of an adjoint pair, and their implementation to boundary value problems for second-order strongly elliptic operators on…
The main objects of our considerations are differential operators generated by a formally selfadjoint differential expression of an even order on the interval $[0,b> (b\leq \infty)$ with operator valued coefficients. We complement and…
We develop a functional model for operators arising in the study of boundary-value problems of materials science and mathematical physics. We then provide explicit formulae for the resolvents of the associated extensions of symmetric…
The abstract theory of self-adjoint extensions of symmetric operators is used to construct self-adjoint realizations of a second-order elliptic operator on $\mathbb{R}^{n}$ with linear boundary conditions on (a relatively open part of) a…
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…
For a second-order symmetric strongly elliptic operator A on a smooth bounded open set \Omega in R^n with boundary \Sigma, the mixed problem is defined by a Neumann-type condition on a part Sigma_+ of the boundary and a Dirichlet condition…
We investigate in the paper general (not necessarily definite) canonical systems of differential equation in the framework of extension theory of symmetric linear relations. For this aim we first introduce the new notion of a boundary…
We prove an analog of Krein's resolvent formula expressing the resolvents of self-adjoint extensions in terms of boundary conditions. Applications to quantum graphs and systems with point interactions are discussed.
We study general (not necessarily Hamiltonian) first-order symmetric systems $J y'(t)-B(t)y(t)=\D(t) f(t)$ on an interval $[a,b> $ with the regular endpoint $a$. The deficiency indices $n_\pm$ of the corresponding minimal relation $\Tmi$…