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Ouvrages Année : 2021

The Feshbach-Schur map and perturbation theory

Résumé

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.
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Dates et versions

hal-03216856 , version 1 (04-05-2021)

Identifiants

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Geneviève Dusson, Israel Michael Sigal, Benjamin Stamm (Dir.). The Feshbach-Schur map and perturbation theory. 2021, Partial Differential Equations, Spectral Theory, and Mathematical Physics, The Ari Laptev Anniversary Volume, ⟨10.4171/ECR/18⟩. ⟨hal-03216856⟩
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