We consider the Galerkin method for approximating the spectrum of an operator where is semi-bounded self-adjoint and satisfies a relative compactness condition. We show that the method is reliable in all regions where it is reliable for the unperturbed problem - which always contains . The results lead to a new technique for identifying eigenvalues of , and for identifying spectral pollution which arises from applying the Galerkin method directly to . The new technique benefits from being applicable on the form domain.
Cite this article
Michael Strauss, The Galerkin method for perturbed self-adjoint operators and applications. J. Spectr. Theory 4 (2014), no. 1, pp. 113–151DOI 10.4171/JST/64