# The Feshbach–Schur map and perturbation theory

@article{Dusson2021TheFM, title={The Feshbach–Schur map and perturbation theory}, author={Genevi{\`e}ve Dusson and Israel Michael Sigal and Benjamin Stamm}, journal={arXiv: Mathematical Physics}, year={2021}, pages={65-88} }

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…

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