Related papers: Essential Spectra of Linear Relations
We describe essential (in particular Fredholm and semi-Fredholm) spectra of operators on Banach lattices of the form $T=wU$, where $w$ is a central operator and $U$ is a disjointness preserving operator such that its spectrum $\sigma(U)$ is…
We characterize the spectrum (and its parts) of operators which can be represented as G=A+BC for a simpler operator A and a structured perturbation BC. The interest in this kind of perturbations is motivated, e.g., by perturbations of the…
Network representations are useful for describing the structure of a large variety of complex systems. Although most studies of real-world networks suppose that nodes are connected by only a single type of edge, most natural and engineered…
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…
An operator $A$ on an $l^p$-space is called band-dominated if it can be approximated, in the operator norm, by operators with a banded matrix representation. The coset of $A$ in the Calkin algebra determines, for example, the Fredholmness…
Some basic facts about Fredholm indices are briefly reviewed, often used in connection with Toeplitz and pseudodifferential operators, and which may be relevant for operators associated to fractals.
The one electron spectral functions for the Luttinger model are discussed for large but finite systems. The methods presented allow a simple interpretation of the results. For finite range interactions interesting nonunivesal spectral…
We consider a Sturm-Liouville operator on a finite interval as well as a scattering problem on the real line both with transfer conditions at the origin. On a finite interval we show that the the Titchmarsh-Weyl $m$-function can be uniquely…
In this paper we show that quasisimilar $n$-tuples of tensor products of $m$-isometric operators have the same spectra, essential spectra and indices. The properties of single Fredholm operators possess \cite{4} is related to an important…
We continue to study $\alpha$-times integrated semigroups. Essentially, we characterize the different spectrums of $\alpha$-times integrated semigroups by the spectrums of their generators. Particulary quasi-Fredholm, Kato, essentially…
Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…
Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
We formalize the general principle of significance with respect to binary relations which is a universal tool for description and analysis of various situations in and apart from mathematics. We derive the basic properties and focus on a…
A model operator $H$ associated to a system describing four particles in interaction, without conservation of the number of particles, is considered. We describe the essential spectrum of $H$ by the spectrum of the channel operators and…
An abstract linking result for Cerami sequences is proved without the Cerami condition. It is applied directly in order to prove the existence of critical points for a class of indefinite problems in infinite dimensional Hilbert Spaces. The…
The spectral properties of a multilevel atomic system interacting with multiple electromagnetic fields, a modified inverted-Y system, have been theoretically investigated. In this study, a numerical matrix propagation method has been…
The relationship between linear relations and matrix pencils is investigated. Given a linear relation, we introduce its Weyr characteristic. If the linear relation is the range (or the kernel) representation of a given matrix pencil, we…
The spectral problem for self-adjoint extensions is studied using the machinery of boundary triplets. For a class of symmetric operators having Weyl functions of a special type we calculate explicitly the spectral projections in the form of…
Let $\mathcal{M}$ be a square matrix over a commutative ring and let $\mathcal{A}$ be a principal submatrix. We give relations between the determinants of $\mathcal{M}$ and $\mathcal{A}$ based on an annihilating polynomial for one of them.…