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We consider some compact non-selfadjoint perturbations of fibered one-dimensional discrete Schr\"odinger operators. We show that the perturbed operator exhibits finite discrete spectrum under suitable\- regularity conditions.

We consider a singular Sturm-Liouville expression with the indefinite weight sgn x. To this expression there is naturally a self-adjoint operator in some Krein space associated. We characterize the local definitizability of this operator in…

Joint spectra of tuples of operators are subsets in complex projective space. The corresponding tuple of operators can be viewed as an infinite dimensional analog of a determinantal representation of the joint spectrum. We investigate the…

We give a spectral description of the semi-classical Schrodinger operator with a piecewise linear, complex valued potential. Moreover, using these results, we show how an arbitrarily small bounded perturbation of a non-self-adjoint operator…

Ordinary and partial differential operators with an indefinite weight function can be viewed as bounded perturbations of non-negative operators in Krein spaces. Under the assumption that 0 and $\infty$ are not singular critical points of…

Given an infinite graph $G$ on countably many vertices, and a closed, infinite set $\Lambda$ of real numbers, we prove the existence of an unbounded self-adjoint operator whose graph is $G$ and whose spectrum is $\Lambda$.

For a Riemannian covering $p \colon M_{2} \to M_{1}$, we compare the spectrum of an essentially self-adjoint differential operator $D_{1}$ on a bundle $E_{1} \to M_{1}$ with the spectrum of its lift $D_{2}$ on $p^{*}E_{1} \to M_{2}$. We…

This article is devoted to the spectral analysis of the electro-magnetic Schr\"odinger operator on the Euclidean plane. In the semiclassical limit, we derive a pseudo-differential effective operator that allows us to describe the spectrum…

This paper is devoted to a general min-max characterization of the eigenvalues in a gap of the essential spectrum of a self-adjoint unbounded operator. We prove an abstract theorem, then we apply it to the case of Dirac operators with a…

We analyze two-dimensional Schr\"odinger operators with the potential $|xy|^p - \lambda (x^2+y^2)^{p/(p+2)}$ where $p\ge 1$ and $\lambda\ge 0$, which exhibit an abrupt change of its spectral properties at a critical value of the coupling…

We consider a self-adjoint operator $T$ on a separable Hilbert space, with pure-point and simple spectrum with accumulations at finite points. Explicit conditions are stated on the eigenvalues of $T$ and on the bounded perturbation $V$…

We continue the investigation of the existence of absolutely continuous (a.c.) spectrum for the discrete Schr\"odinger operator $\Delta+V$ on $\ell^2(\Z^d)$, in dimensions $d\geq 2$, for potentials $V$ satisfying the long range condition…

We consider a quadratic operator pencil with a small periodic perturbation multiplied by the spectral parameter. It is motivated, in particular, by a one-dimensional Klein-Gordon equation with a time-parity-symmetric perturbation. We study…

In this paper we explore a certain class of non-selfadjoint operators acting in a complex separable Hilbert space. We consider a perturbation of a non-selfadjoint operator by an operator that is also non-selfadjoint. Our consideration is…

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…

In this paper we consider the spectrum of the self-adjoint differential operator L generated by the differential expression of order n with the m by m periodic matrix coefficients, where n and m are respectively odd and even integers and…

We consider a $2\times2$ block operator matrix ${\mathcal A}_\mu$ $($$\mu>0$ is a coupling constant$)$ acting in the direct sum of one- and two-particle subspaces of a bosonic Fock space. The location of the essential spectrum of ${\mathcal…

We discuss the essential spectrum of essentially self-adjoint elliptic differential operators of first order and of Laplace type operators on Riemannian vector bundles over geometrically finite orbifolds.

We study the distribution of the eigenvalues inside of the essential spectrum for discrete one-dimensional Schr\"odinger operators with potentials of Coulomb type decay.

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…