Related papers: Spectral algebraic curves and decomposable operato…

We consider non-self-adjoint operators in Hilbert spaces of the form $H=H_0+CWC$, where $H_0$ is self-adjoint, $W$ is bounded and $C$ is a metric operator, $C$ bounded and relatively compact with respect to $H_0$. We suppose that…

We study spectral theory for bounded Borel subsets of $\br$ and in particular finite unions of intervals. For Hilbert space, we take $L^2$ of the union of the intervals. This yields a boundary value problem arising from the minimal operator…

We develop a new approach to the study of spectral asymmetry. Working with the operator $\operatorname{curl}:=*\mathrm{d}$ on a connected oriented closed Riemannian 3-manifold, we construct, by means of microlocal analysis, the asymmetry…

We show that 2D periodic operators with local and perpendicular defects form an algebra. We provide an algorithm of finding spectrum for such operators. While the continuous spectral components can be computed by simple algebraic operations…

We look at various forms of spectrum and associated pseudospectrum that can be defined for noncommuting $d$-tuples of Hermitian elements of a $C^*$-algebra. The emphasis is on theoretical calculations of examples, in particular for…

We extend the concept of Lifshits--Krein spectral shift function associated with a pair of self-adjoint operators to the case of pairs of admissible operators that are similar to self-adjoint operators. Our main result is the following. Let…

In this article we discuss a few spectral properties of a paranormal closed operator (not necessarily bounded) defined in a Hilbert space. This class contains closed symmetric operators. First we show that the spectrum of such an operator…

Spectral theory and functional calculus for unbounded self-adjoint operators on a Hilbert space are usually treated through von Neumann's Cayley transform. Based on ideas of Woronowicz, we redevelop this theory from the point of view of…

We consider problems associated with the computation of spectra of self-adjoint operators in terms of the eigenvalue distributions of their n x n sections. Under rather general circumstances, we show how these eigenvalues accumulate near…

We give necessary and sufficient conditions for real sequences to be the spectra of selfadjoint extensions of an entire operator whose domain may be non-dense. For this spectral characterization we use de Branges space techniques and a…

In a real Hilbert spaces H a smooth operator F is studied, whose derivative at each point of its domain is a symmetric operator. In terms of abstract boundary conditions locally self-adjoint extensions of this operator are described. We use…

By means of the operator extension theory, we construct an explicitly solvable model of a simple-cubic three-dimensional regimented array of quantum dots in the presence of a uniform magnetic field. The spectral properties of the model are…

Given a pair of smooth transversally intersecting manifolds in some ambient manifold, we construct an operator algebra generated by pseudodifferential operators and the (co)boundary operators associated with the submanifolds. We show that…

In this paper, we consider real and complex algebras as well as algebras over general fields. In Section 2, we revisit and prove several results on (quadratic) algebras over general fields. As an example, we demonstrate that a quadratic…

Spectra of the second derivative operators corresponding to the special PT-symmetric point interactions are studied. The results are partly the completion of those obtained in [1]. The particular PT-symmetric point interactions causing…

This paper introduces and investigates the concept of the $q$-numerical range for tuples of bounded linear operators in Hilbert spaces. We establish various inequalities concerning the $q$-numerical radius associated with these operator…

We analyze the spectrum of the operator $\Delta^{-1} [\nabla \cdot (K\nabla u)]$, where $\Delta$ denotes the Laplacian and $K=K(x,y)$ is a symmetric tensor. Our main result shows that this spectrum can be derived from the spectral…

In this paper we develop a version of spectral theory for bounded linear operators on topological vector spaces. We show that the Gelfand formula for spectral radius and Neumann series can still be naturally interpreted for operators on…

Let $u=\int_{-\infty}^{+\infty}\lambda dE_{\lambda}$ be a self-adjoint operator in a Hilbert space $H$. Our purpose is to provide a non-standard description of the spectral family $(E_{\lambda})$ and the generalized Gelfand eigenvectors.

In this paper we extend the traditional framework of noncommutative geometry in order to deal with spectral truncations of geometric spaces (i.e. imposing an ultraviolet cutoff in momentum space) and with tolerance relations which provide a…