Related papers: Spectral gaps for self-adjoint second order operat…

For the magnetic Laplacian on a bounded planar domain, imposing Neumann boundary conditions produces eigenvalues below the lowest Landau level. If the domain has two boundary components and one imposes a Neumann condition on one component…

This paper addresses two different but related questions regarding an unbounded symmetric tridiagonal operator: its self-adjointness and the approximation of its spectrum by the eigenvalues of its finite truncations. The sufficient…

A fundamental result of Solomyak says that the number of negative eigenvalues of a Schr\"odinger operator on a two-dimensional domain is bounded from above by a constant times a certain Orlicz norm of the potential. Here we show that in the…

In this paper we study spectral properties of Dirichlet-to-Neumann map on differential forms obtained by a slight modification of the definition due to Belishev and Sharafutdinov. The resulting operator $\Lambda$ is shown to be self-adjoint…

Eigenvalue problems for semidefinite operators with infinite dimensional kernels appear for instance in electromagnetics. Variational discretizations with edge elements have long been analyzed in terms of a discrete compactness property. As…

We study the effect of non-negative potentials on the spectral gap of one-dimensional Schr\"odinger operators in the limit of large intervals. In particular, we derive upper and lower bounds on the gap for different classes of potentials…

We study the selfadjoint extensions of the spatial part of the D'Alembert operator in a spacetime with two changes of signature. We identify a set of boundary conditions, parametrised by U(2) matrices, which correspond to Dirichlet boundary…

We prove estimates for the variation of the eigenvalues of uniformly elliptic operators with homogeneous Dirichlet or Neumann boundary conditions upon variation of the open set on which an operator is defined. We consider operators of…

It is well known that the standard projection methods allow one to recover the whole spectrum of a bounded self-adjoint operator but they often lead to spectral pollution, i.e. to spurious eigenvalues lying in the gaps of the essential…

We define a class of pseudo-ergodic non-self-adjoint Schr\"odinger operators acting in spaces $l^2(X)$ and prove some general theorems about their spectral properties. We then apply these to study the spectrum of a non-self-adjoint Anderson…

We introduce the notion of a pre-spectral triple, which is a generalisation of a spectral triple $(\mathcal{A}, H, D)$ where $D$ is no longer required to be self-adjoint, but closed and symmetric. Despite having weaker assumptions,…

We study the trace class perturbations of the half-line, discrete Laplacian and obtain a new bound for the perturbation determinant of the corresponding non-self-adjoint Jacobi operator. Based on this bound, we obtain the Lieb--Thirring…

We consider the problem of how to compute eigenvalues of a self-adjoint operator when a direct application of the Galerkin (finite-section) method is unreliable. The last two decades have seen the development of the so-called quadratic…

We study a family of differential operators $L_\alpha$ in two variables, depending on the coupling parameter $\alpha\ge0$ that appears only in the boundary conditions. Our main concern is the spectral properties of $L_\alpha$, which turn…

Let A be a self-adjoint operator on a Hilbert space H. Assume that {\sigma} is an isolated component of the spectrum of A, i.e. dist({\sigma},{\Sigma})=d>0 where {\Sigma}=spec(A)\{\sigma}. Suppose that V is a bounded self-adjoint operator…

We analyze the spectrum of the Neumann-Poincar\'e (NP) operator for a doubly connected domain lying between two level curves defined by a conformal mapping, where the inner boundary of the domain is of general shape. The analysis relies on…

The paper deals with a Dirichlet spectral problem for a singularly perturbed second order elliptic operator with rapidly oscillating locally periodic coefficients. We study the limit behaviour of the first eigenpair (ground state) of this…

For a class of non-selfadjoint semiclassical operators in dimension one, we get a complete asymptotic description of all eigenvalues near a critical value of the leading symbol of the operator on the boundary of the pseudospectrum.

We present a model for spectral theory of families of selfadjoint operators, and their corresponding unitary one-parameter groups (acting in Hilbert space.) The models allow for a scale of complexity, indexed by the natural numbers…

For a given self-adjoint operator $A$ with discrete spectrum, we completely characterize possible eigenvalues of its rank-one perturbations~$B$ and discuss the inverse problem of reconstructing $B$ from its spectrum.