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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