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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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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spelling ndltd-CALTECH-oai-thesis.library.caltech.edu-40482021-04-17T05:01:46Z https://thesis.library.caltech.edu/4048/ Boundary behavior of Cauchy integrals and rank one perturbations of operators Poltoratski, Alexei G. 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. 1995 Thesis NonPeerReviewed application/pdf en other 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> https://resolver.caltech.edu/CaltechETD:etd-10122007-080912 CaltechETD:etd-10122007-080912 10.7907/xm4x-r304
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language en
format Others
sources NDLTD
description 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.
author Poltoratski, Alexei G.
spellingShingle Poltoratski, Alexei G.
Boundary behavior of Cauchy integrals and rank one perturbations of operators
author_facet Poltoratski, Alexei G.
author_sort Poltoratski, Alexei G.
title Boundary behavior of Cauchy integrals and rank one perturbations of operators
title_short Boundary behavior of Cauchy integrals and rank one perturbations of operators
title_full Boundary behavior of Cauchy integrals and rank one perturbations of operators
title_fullStr Boundary behavior of Cauchy integrals and rank one perturbations of operators
title_full_unstemmed Boundary behavior of Cauchy integrals and rank one perturbations of operators
title_sort boundary behavior of cauchy integrals and rank one perturbations of operators
publishDate 1995
url 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>
work_keys_str_mv AT poltoratskialexeig boundarybehaviorofcauchyintegralsandrankoneperturbationsofoperators
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