Citation
Wong, Manwah Lilian (2009) Orthogonal polynomials, paraorthogonal polynomials and point perturbation. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd06092009004344
Abstract
This thesis consists of three parts.
Part 1 starts with an introduction to orthogonal polynomials, to be followed by some wellknown theorems pertinent to the results we shall discuss. It also states the new results that are going to be proven in Parts 2 and 3.
In Part 2, we consider a sequence of paraorthogonal polynomials and investigate their zeros. Then we introduce paraorthogonal polynomials of the second kind and prove that zeros of ﬁrst and second kind paraorthogonal polynomials interlace.
In Part 3, we consider the point mass problem. First, we give the point mass formula for the perturbed Verblunsky coefficients. Then we investigate the asymptotics of orthogonal polynomials on the unit circle and apply the results to the point mass formula to compute the perturbed Verblunsky coefficients. Finally, we present two examples, one on the unit circle and one on the real line, such that adding a point mass will generate nonexponential perturbations of the recursion coefficients.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  paraorthogonal polynomials; point perturbation 
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:  27 May 2009 
Author Email:  wongmw (AT) alumni.princeton.edu 
Record Number:  CaltechETD:etd06092009004344 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd06092009004344 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  5229 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  18 Jun 2009 
Last Modified:  26 Dec 2012 03:16 
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