Citation
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
Abstract
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.
| Item Type: | Thesis (Dissertation (Ph.D.)) |
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| Degree Grantor: | California Institute of Technology |
| Division: | Physics, Mathematics and Astronomy |
| Major Option: | Mathematics |
| Thesis Availability: | Public (worldwide access) |
| Research Advisor(s): |
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| Thesis Committee: |
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| Defense Date: | 5 May 1995 |
| Record Number: | CaltechETD:etd-10122007-080912 |
| Persistent URL: | https://resolver.caltech.edu/CaltechETD:etd-10122007-080912 |
| DOI: | 10.7907/xm4x-r304 |
| Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
| ID Code: | 4048 |
| Collection: | CaltechTHESIS |
| Deposited By: | Imported from ETD-db |
| Deposited On: | 25 Oct 2007 |
| Last Modified: | 16 Apr 2021 22:56 |
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