Rank one and finite rank perturbations - survey and open problems

2012/05/20 by Constanze Liaw, Liaw, Constanze
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #math-ph #math.FA #math.MP #math.SP

paper · pdf · doi:10.48550/arxiv.1205.4376

17 pages

arxiv created 2012/05/20 · arxiv updated 2012/05/22

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.

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