Strong Asymptotics for Extremal Polynomials Associated with Weights on R by Doron S. LubinskyStrong Asymptotics for Extremal Polynomials Associated with Weights on R by Doron S. Lubinsky

Strong Asymptotics for Extremal Polynomials Associated with Weights on R

byDoron S. Lubinsky, Edward B. Saff

Paperback | March 9, 1988

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0. The results are consequences of a strengthened form of the following assertion: Given 0 <_2c_ f="" lp="" _28_="" _29_="" and="" a="" certain="" sequence="" of="" positive="" numbers="" associated="" with="" _q28_x29_2c_="" there="" exist="" polynomials="" pn="" degree="" at="" most="" _n2c_="" n="1%2c2%2c3...%2c" such="" that="" if="" only="" _f28_x29_="0" for="" a.e.=""> 1. Auxiliary results include inequalities for weighted polynomials, and zeros of extremal polynomials. The monograph is fairly self-contained, with proofs involving elementary complex analysis, and the theory of orthogonal and extremal polynomials. It should be of interest to research workers in approximation theory and orthogonal polynomials.
Title:Strong Asymptotics for Extremal Polynomials Associated with Weights on RFormat:PaperbackDimensions:160 pagesPublished:March 9, 1988Publisher:Springer Berlin HeidelbergLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3540189580

ISBN - 13:9783540189589

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Table of Contents

Notation and index of notation.- Statement of main results.- Weighted polynomials and zeros of extremal polynomials.- Integral equations.- Polynomial approximation of potentials.- Infinite-finite range inequalities and their sharpness.- The largest zeros of extremal polynomials.- Further properties of Un, R(x).- Nth root asymptotics for extremal polynomials.- Approximation by certain weighted polynomials, I.- Approximation by certain weighted polynomials, II.- Bernstein's formula and bernstein extremal polynomials.- Proof of the asymptotics for Enp(W).- Proof of the asymptotics for the Lp extremal polynomials.- The case p=2 : Orthonormal polynomials.