Boundary behavior of Cauchy integrals and rank one perturbations of operators

Author: Poltoratski, Alexei G.

Year: 1995

Degree: Dissertation (Ph.D.)

Advisor: Makarov, Nikolai G.

Committee Member: Unknown, Unknown

Option: Mathematics

DOI: 10.7907/xm4x-r304

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.

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