Related papers: A survey on the resolvent convergence

We consider a second order self-adjoint operator in a domain which can be bounded or unbounded. The boundary is partitioned into two parts with Dirichlet boundary condition on one of them, and Neumann condition on the other. We assume that…

We consider Schr\"odinger operators on a bounded, smooth domain of dimension $d \ge 2$ with Dirichlet boundary conditions and a properly scaled potential, which depends only on the distance to the boundary of the domain. Our aim is to…

In the present paper we investigate the set $\Sigma_J$ of all $J$-self-adjoint extensions of a symmetric operator $S$ with deficiency indices $<2,2>$ which commutes with a non-trivial fundamental symmetry $J$ of a Krein space…

Let $B$ be a bounded self-adjoint operator and let $A$ be a nonnegative self-adjoint unbounded operator. It is shown that if $BA$ is normal, it must be self-adjoint and so must be $AB$. Commutativity is necessary and sufficient for this…

The paper deals with homogenisation problems for high-contrast symmetric convolution-type operators with integrable kernels in media with a periodic microstructure. We adapt the two-scale convergence method to nonlocal convolution-type…

If $T$ is a semibounded self-adjoint operator in a Hilbert space $(H, \, (\cdot , \cdot))$ then the closure of the sesquilinear form $(T \cdot , \cdot)$ is a unique Hilbert space completion. In the non-semibounded case a closure is a…

The goal of this note is to study the spectrum of a self-adjoint convolution operator in $L^2(\mathbb R^d)$ with an integrable kernel that is perturbed by an essentially bounded real-valued potential tending to zero at infinity. We show…

The main goal of this paper is to show that a (not necessarily densely defined or closed) symmetric operator $A$ acting on a real or complex Hilbert space is selfadjoint exactly when $I+A^2$ is a full range operator.

We present a convergence theory for Optimized Schwarz Methods that rely on a non-local exchange operator and covers the case of coercive possibly non-self-adjoint impedance operators. This analysis also naturally deals with the presence of…

Action convergence provides a limit theory for linear bounded operators $A_n:L^{\infty}(\Omega_n)\longrightarrow L^1(\Omega_n)$ where $\Omega_n$ are potentially different probability spaces. This notion of convergence emerged in graph…

Given a densely defined and closed operator $A$ acting on a complex Hilbert space $\mathcal{H}$, we establish a one-to-one correspondence between its closed extensions and subspaces $\mathfrak{M}\subset\mathcal{D}(A^*)$, that are closed…

We consider a non-relativistic quantum particle in $\mathbb{R}^d$, $d=2$ or $d = 3$, interacting with singular zero-range potentials concentrated on a large collection of points. We analyze the homogenization regime where the intensities of…

This work develops a functional-analytic framework based on the transfinite iteration of a self-adjoint operator. Beginning with a densely defined self-adjoint operator $A$ on a Hilbert space $H$, a spectral-transform functor $\Phi$ is…

We introduce kernels and resolvents on preordered sets and derive sharp resolvent inequalities that entail Gronwall inequalities for functions of several variables. In this way, we can prove a fixed point result for operators on topological…

Devinatz, Nussbaum and von Neumann established some important results on the strong commutativity of self-adjoint and normal unbounded operators. In this paper, we prove results in the same spirit.

We prove quantitative bounds on the eigenvalues of non-selfadjoint bounded and unbounded operators. We use the perturbation determinant to reduce the problem to one of studying the zeroes of a holomorphic function.

We define direct sums and a corresponding notion of connectedness for graph limits. Every graph limit has a unique decomposition as a direct sum of connected components. As is well-known, graph limits may be represented by symmetric…

A special class of generalized Jacobi operators which are self-adjoint in Krein spaces is presented. A description of the resolvent set of such operators in terms of solutions of the corresponding recurrence relations is given. In…

We establish the convergence of the resolvent of the Reissner-Mindlin system in any dimension $N \geq 2$, with any of the physically relevant boundary conditions, to the resolvent of the biharmonic operator with suitably defined boundary…

A characterization of the essential spectrum $\sigma_{\text ess}$ of Schr\"odinger operators on infinite graphs is derived involving the concept of $\mathcal{R}$-limits. This concept, which was introduced previously for operators on…