Boundary behavior of Cauchy integrals and rank one perturbations of operators

Boundary behavior of Cauchy integrals and rank one perturbations of operators

We develop new methods based on Rohlin-type decompositions of Lebesgue measure on the unit circle and on the real line to study the boundary behavior of Cauchy integrals. We also apply these methods to investigate the notion of Krein spectral shift of a self-adjoint operator. Using this notion we...

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Bibliographic Details
Main Author: Poltoratski, Alexei G.
Format: Others
Language:en
Published: 1995
Online Access:https://thesis.library.caltech.edu/4048/1/Poltoratski_a_1995.pdf
Poltoratski, Alexei G. (1995) Boundary behavior of Cauchy integrals and rank one perturbations of operators. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/xm4x-r304. https://resolver.caltech.edu/CaltechETD:etd-10122007-080912 <https://resolver.caltech.edu/CaltechETD:etd-10122007-080912>
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Summary:We develop new methods based on Rohlin-type decompositions of Lebesgue measure on the unit circle and on the real line to study the boundary behavior of Cauchy integrals. We also apply these methods to investigate the notion of Krein spectral shift of a self-adjoint operator. Using this notion we study the spectral properties of rank one perturbations of operators.

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