Generalised Weyl theorems and spectral pollution in the Galerkin method

Details Generalised Weyl theorems and spectral pollution in the Galerkin method Generalised Weyl theorems and spectral pollution in the Galerkin method

2010-11-16

arxiv.org/abs/1011.3634v2

Mathematics

Spectral Theory

The new version deals with Galerkin sequences which are dense in the form domain of A, when A is bounded from below

Scientific paper

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.

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