Notes on Rank-One Perturbed Resolvent
Mathematical Physics
2016-09-07 v3 Dynamical Systems
math.MP
Abstract
This paper is a didactic comment (a transcription with variations) to the paper of S.R. Foguel {\it Finite Dimensional Perturbations in Banach Spaces}. Addressed, mainly: postgraduates and related readers. Subject: Suppose we have two linear operators, T_1, T_2, so that T_2^{-1} - T_1^{-1} is rank-one. What we want to know is how we can express (z-T_2)^{-1} in terms of T_2^{-1} - T_1^{-1} and (z-T_1)^{-1} . Keywords: M.G.Krein's Formula, Finite Rank Perturbations.
Cite
@article{arxiv.math-ph/0312016,
title = {Notes on Rank-One Perturbed Resolvent},
author = {Sergej A. Choroszavin},
journal= {arXiv preprint arXiv:math-ph/0312016},
year = {2016}
}
Comments
Latex 2.09, one misprint corrected