An Overview of Periodic Elliptic Operators

Spectral Gaps for Periodic Elliptic Operators with High Contrast: an Overview

We discuss the band-gap structure and the integrated density of states for periodic elliptic operators in the Hilbert space L2(R m), for m ≥ 2. We specifically consider situations where high contrast in the coefficients leads to weak coupling between the period cells. Weak coupling of periodic systems frequently produces spectral gaps or spectral concentration. Our examples include Schrödinger ...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

Asymptotic distribution of eigenvalues of the elliptic operator system

Since the theory of spectral properties of non-self-accession differential operators on Sobolev spaces is an important field in mathematics, therefore, different techniques are used to study them. In this paper, two types of non-self-accession differential operators on Sobolev spaces are considered and their spectral properties are investigated with two different and new techniques.

ar X iv : m at h - ph / 9 90 10 11 v 2 2 9 Ju n 19 99 NON - COMMUTATIVE BLOCH THEORY : AN OVERVIEW

For differential operators which are invariant under the action of an abelian group Bloch theory is the tool of choice to analyze spectral properties. By shedding some new non-commutative light on this we motivate the introduction of a noncommutative Bloch theory for elliptic operators on Hilbert C-modules. It relates properties of C-algebras to spectral properties of module operators such as b...

On the Structure of Spectra of Periodic Elliptic Operators

The paper discusses the problem of absolute continuity of spectra of periodic elliptic operators. A new result on absolute continuity for a matrix operator of Schrödinger type is obtained. It is shown that all types of operators for which the absolute continuity has previously been established can be reduced to this one. It is also discovered that some natural generalizations stumble upon an ob...