Perturbation of Spectra

Abstract

The method of perturbation is one of the most effective methods of determining approximately the spectral representation of a given operator. The method is applicable if the operator L in question is sufficiently near another operator L₀ whose spectral representation is known — or partly known. One then introduces an operator L_ε which depends on a parameter ε in such a way that it reduces to L for ε = 1 and to L₀ for ε = 0. Then one tries to expand the spectral representers of L _ε in powers of ε. The approximate representers of L are obtained by breaking off the series after a few terms and then setting ε = 1.