Citation
Lukic, Milivoje (2011) Spectral theory for generalized bounded variation perturbations of orthogonal polynomials and Schrodinger operators. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:05262011194849007
Abstract
The purpose of this text is to present some new results in the spectral theory of orthogonal polynomials and Schrodinger operators. These results concern perturbations of the free Schrodinger operator and of the free case for orthogonal polynomials on the unit circle (which corresponds to Verblunsky coefficients equal to 0) and the real line (which corresponds to offdiagonal Jacobi coefficients equal to 1 and diagonal Jacobi coefficients equal to 0). The condition central to our results is that of generalized bounded variation. This class consists of finite linear combinations of sequences of rotated bounded variation with an L^1 perturbation. This generalizes both usual bounded variation and expressions of the form lambda(x) cos(phi x + alpha) with lambda(x) of bounded variation (and, in particular, with lambda(x) = x^gamma, Wignervon Neumann potentials) as well as their finite linear combinations. Assuming generalized bounded variation and an L^p condition (with any finite p) on the perturbation, our results show preservation of absolutely continuous spectrum, absence of singular continuous spectrum, and that embedded pure points in the continuous spectrum can only occur in an explicit finite set.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  spectral theory, orthogonal polynomials, Schrodinger operators, bounded variation, Wignervon Neumann potential 
Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Mathematics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  18 May 2011 
Author Email:  milivoje.lukic (AT) gmail.com 
Record Number:  CaltechTHESIS:05262011194849007 
Persistent URL:  http://resolver.caltech.edu/CaltechTHESIS:05262011194849007 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  6460 
Collection:  CaltechTHESIS 
Deposited By:  Milivoje Lukic 
Deposited On:  27 May 2011 21:52 
Last Modified:  26 Dec 2012 04:36 
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