Related papers: One-dimensional perturbations of unbounded selfadj…

We consider the self-adjoint fourth-order operator with real $1$-periodic coefficients on the unit interval. The spectrum of this operator is discrete. We determine the high energy asymptotics for its eigenvalues.

We study the behaviour of functions of pairs of commuting self-adjoint operators under perturbations by relatively bounded operators. We obtain analogs of our earlier results for functions of a single self-adjoint operator under relatively…

We develop the method of similar operators to study the spectral properties of unbounded perturbed linear operators that can be represented by matrices of various kinds. The class of operators under consideration includes various…

In this paper spectral theorems for not necessarily continuous normal and self-adjoint random operators on a complex separable Hilbert space are proved.

This paper analyzes the scattering matrix for two unbounded self-adjoint operators: the standard Laplace operator in three-dimensional space and a second operator that differs from the first by an infinite sum of zero-range potentials.

This paper deals with the generalized spectrum of continuously invertible linear operators defined on infinite dimensional Hilbert spaces. More precisely, we consider two bounded, coercive, and self-adjoint operators $\bc{A, B}: V\mapsto…

The aim of this article is to present a brief overview of spectral perturbation theory for matrices, bounded linear operators and holomorphic operator-valued functions. We focus on bounds for perturbed eigenvalues, eigenvectors and…

We give a precise and complete description on the spectrum for a class of non-self-adjoint quasi-periodic operators acting on $\ell^2(\mathbb{Z}^d)$ which contains the Sarnak's model as a special case. As a consequence, one can see various…

This paper is devoted to the definition and analysis of the spectral shift function (SSF) associated with non-self-adjoint perturbations of self-adjoint operators. Motivated by applications in scattering theory, we consider both trace-class…

We introduce compactness classes of Hilbert space operators by grouping together all operators for which the associated singular values decay at a certain speed and establish upper bounds for the norm of the resolvent of operators belonging…

We prove that there exists a rank one perturbation of a unitary operator on a complex separable infinite dimensional Hilbert space which is hypercyclic.

Partial operators can have void or unbounded spectra. Contrarily to what is written in Dunford-Schwarz, the reason is not in the fact they are unounded operators.

We prove and apply two theorems: First, a quantitative, scale-free unique continuation estimate for functions in a spectral subspace of a Schr\"odinger operator on a bounded or unbounded domain, second, a perturbation and lifting estimate…

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 $\Lambda$.

Affiliated and normal operators in octonion Hilbert spaces are studied. Theorems about their properties and of related algebras are demonstrated. Spectra of unbounded normal operators are investigated.

We define Dirac operators on $\mathbb{S}^3$ (and $\mathbb{R}^3$) with magnetic fields supported on smooth, oriented links and prove self-adjointness of certain (natural) extensions. We then analyze their spectral properties and show, among…

Spectrum of the volume integral operator of the three-dimensional electromagnetic scattering is analyzed. The operator has both continuous essential spectrum, which dominates at lower frequencies, and discrete eigenvalues, which spread out…

Given a self-adjoint operator $T$ on a separable infinite-dimensional Hilbert space we study the problem of characterizing the set $\mathcal D(T)$ of all possible diagonals of $T$. For operators $T$ with at least two points in their…

Non-self-adjoint Schrodinger operators which correspond to non-symmetric zero-range potentials are investigated. We show that various properties of these operators (eigenvalues, exceptional points, spectral singularities and the property of…

We study singular Schrodinger operators with an attractive interaction supported by a closed smooth surface A in R^3 and analyze their behavior in the vicinity of the critical situation where such an operator has empty discrete spectrum and…