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Boundary behavior of Cauchy integrals and rank one perturbations of operators


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.


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.))
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Makarov, Nikolai G.
Thesis Committee:
  • Unknown, Unknown
Defense Date:5 May 1995
Record Number:CaltechETD:etd-10122007-080912
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4048
Deposited By: Imported from ETD-db
Deposited On:25 Oct 2007
Last Modified:16 Apr 2021 22:56

Thesis Files

PDF (Poltoratski_a_1995.pdf) - Final Version
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