Related papers: The essential spectrum of the Laplacian

In this article we prove a generalization of Weyl's criterion for the spectrum of a self-adjoint nonnegative operator on a Hilbert space. We will apply this new criterion in combination with Cheeger-Fukaya-Gromov and Cheeger-Colding theory…

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 consider a non self-adjoint Laplacian on a directed graph with non symmetric edge weights. We give necessary conditions for this Laplacian to be sectorial. We introduce a special self-adjoint operator and compare its essential spectrum…

We prove a new criterion for the essential self-adjointness of pseudodifferential operators that does not involve ellipticity-type assumptions. For example, we show that self-adjointness holds in case the symbol is $C^{2d+3}$ with…

In this paper we consider a family of Riemannian manifolds, not necessarily complete, with curvature conditions in a neighborhood of a ray. Under these conditions we obtain that the essential spectrum of the Laplacian contains an interval.…

The spectrum of a selfadjoint second order elliptic differential operator in $L^2(\mathbb{R}^n)$ is described in terms of the limiting behavior of Dirichlet-to-Neumann maps, which arise in a multi-dimensional Glazman decomposition and…

The spectral properties of non-self-adjoint extensions $A_{[B]}$ of a symmetric operator in a Hilbert space are studied with the help of ordinary and quasi boundary triples and the corresponding Weyl functions. These extensions are given in…

In this article, we find sufficient conditions on an open Riemannian manifold so that a Weyl criterion holds for the $L^p$-spectrum of the Laplacian on $k$-forms, and also prove the decomposition of the $L^p$-spectrum depending on the order…

We consider an arbitrary selfadjoint operator on a separable Hilbert space. To this operator we construct an expansion in generalized eigenfunctions in which the original Hilbert space is decomposed as a direct integral of Hilbert spaces…

We consider the Laplace operator in a planar waveguide, i.e., an infinite two-dimensional straight strip of constant width, with particular types of Robin boundary conditions. We study the essential spectrum of the corresponding Laplacian…

In this paper, we investigate the spectrum of a class of weighted Laplacians on Cayley graphs and determine under what conditions the corresponding eigenspaces are generically irreducible. Specifically, we analyze the spectrum on…

In this paper, we investigate spectral properties of discrete Laplacians. Our study is based on the Hardy inequality and the use of super-harmonic functions. We recover and improve lower bounds for the bottom of the spectrum and of the…

Motivated by recent interest in the spectrum of the Laplacian of incomplete surfaces with isolated conical singularities, we consider more general incomplete m-dimensional manifolds with singularities on sets of codimension at least 2. With…

The purpose of this paper is to study the essential spectrum of non-self-adjoint singular matrix differential operators in the Hilbert space $L^2(\mathbb{R})\oplus L^2(\mathbb{R})$ induced by matrix differential expressions of the form…

For a sequence of self--adjoint operators, which converges in the norm resolvent sense, the formula is derived, which expresses the essential spectrum of the limit through the essential spectrum of the elements of the sequence.

We consider the Dirichlet Laplacian in a domain two three-dimensional parallel layers having common boundary and coupled by a window. The window produces the bound states below the essential spectrum; we obtain two-sided estimates for them.…

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…

We isolate a large class of self-adjoint operators H whose essential spectrum is determined by their behavior at large x and we give a canonical representation of their essential spectrum in terms of spectra of limits at infinity of…

Let $H_0$ and $H$ be self-adjoint operators in a Hilbert space. In the scattering theory framework, we describe the essential spectrum of the difference $\varphi(H)-\varphi(H_0)$ for piecewise continuous functions $\varphi$. This…

A new proof of the Weyl limit point-limit circle criterion is obtained, with systematic emphasis on Sobolev-space methods.