The Feshbach-Schur map and perturbation theory
Abstract
This paper deals with perturbation theory for discrete spectra of linear operators. To simplify exposition we consider here self-adjoint operators. This theory is based on the Feshbach-Schur map and it has advantages with respect to the standard perturbation theory in three aspects: (a) it readily produces rigorous estimates on eigenvalues and eigenfunctions with explicit constants; (b) it is compact and elementary (it uses properties of norms and the fundamental theorem of algebra about solutions of polynomial equations); and (c) it is based on a self-contained formulation of a fixed point problem for the eigenvalues and eigenfunctions, allowing for easy iterations. We apply our abstract results to obtain rigorous bounds on the ground states of Helium-type ions.
Keywords
Cite
@article{arxiv.2105.02058,
title = {The Feshbach-Schur map and perturbation theory},
author = {Geneviève Dusson and Israel Sigal and Benjamin Stamm},
journal= {arXiv preprint arXiv:2105.02058},
year = {2021}
}