Rank one and finite rank perturbations - survey and open problems
Spectral Theory
2012-05-22 v1 Mathematical Physics
Functional Analysis
math.MP
Abstract
We survey the relationships of rank one self-adjoint and unitary perturbations as well as finite rank unitary perturbations with various branches of analysis and mathematical physics. We include the case of non-inner characteristic operator functions. For rank one perturbations and non-inner characteristic functions, we prove a representation formula for the adjoint of the Clark operator. Throughout we mention many open problems at varying levels of difficulty.
Keywords
Cite
@article{arxiv.1205.4376,
title = {Rank one and finite rank perturbations - survey and open problems},
author = {Constanze Liaw},
journal= {arXiv preprint arXiv:1205.4376},
year = {2012}
}
Comments
17 pages