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作者 Simanek, Brian
書名 Asymptotic Properties of Orthogonal and Extremal Polynomials
國際標準書號 9781267355317
book jacket
說明 116 p
附註 Source: Dissertation Abstracts International, Volume: 73-09, 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 define---for each natural number n---a monic polynomial of degree n having minimum Lq-norm 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 73-09B
主題 Mathematics
Theoretical Mathematics
0405
0642
Alt Author California Institute of Technology. Mathematics
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