Generalised Weyl theorems and spectral pollution in the Galerkin method
Spectral Theory
2012-07-11 v2
Abstract
We consider a general framework for investigating spectral pollution in the Galerkin method. We show how this phenomenon is characterised via the existence of particular Weyl sequences which are singular in a suitable sense. For a semi-bounded selfadjoint operator A we identify relative compactness conditions on a selfadjoint perturbation B ensuring that the limiting set of spectral pollution of A and B coincide. Our results show that, under perturbation, this limiting set behaves in a similar fashion as the essential spectrum.
Keywords
Cite
@article{arxiv.1011.3634,
title = {Generalised Weyl theorems and spectral pollution in the Galerkin method},
author = {Lyonell Boulton and Nabile Boussaid and Mathieu Lewin},
journal= {arXiv preprint arXiv:1011.3634},
year = {2012}
}
Comments
The new version deals with Galerkin sequences which are dense in the form domain of A, when A is bounded from below