說明 
116 p 
附註 
Source: Dissertation Abstracts International, Volume: 7309, Section: B, page: 

Adviser: Barry M. Simon 

Thesis (Ph.D.)California Institute of Technology, 2012 

This thesis describes the asymptotic behavior of extremal polynomials in a variety of settings. Special attention is given to the orthonormal and monic orthogonal polynomials. Given a measure with compact and infinite support in the complex plane and a positive real number q, one can definefor each natural number na monic polynomial of degree n having minimum Lqnorm with respect to the given measure among all monic polynomials of the same degree. Dividing this extremal polynomial by its norm produces a normalized extremal polynomial of degree n. We will describe the asymptotic behavior of the extremal polynomials when the given measure is of a certain very general form. Our new results concerning the extremal polynomial asymptotics will include Szego asymptotics, ratio asymptotics, and relative asymptotics. We will also describe the asymptotic behavior of the associated Christoffel functions and describe the weak asymptotic behavior of sequences of measures derived from the normalized extremal polynomials 

School code: 0037 
Host Item 
Dissertation Abstracts International 7309B

主題 
Mathematics


Theoretical Mathematics


0405


0642

Alt Author 
California Institute of Technology. Mathematics

