JournalsjstVol. 4, No. 1pp. 113–151

The Galerkin method for perturbed self-adjoint operators and applications

  • Michael Strauss

    Glasgow, UK
The Galerkin method for perturbed self-adjoint operators and applications cover
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Abstract

We consider the Galerkin method for approximating the spectrum of an operator T+AT+A where TT is semi-bounded self-adjoint and AA 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 C\R\mathbb{C}\backslash\mathbb{R}. The results lead to a new technique for identifying eigenvalues of TT, and for identifying spectral pollution which arises from applying the Galerkin method directly to TT. 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. 113–151

DOI 10.4171/JST/64