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＜E-Book＞
Strong Asymptotics for Extremal Polynomials Associated with Weights on R / by Doron S. Lubinsky, Edward B. Saff
(Lecture Notes in Mathematics. ISSN:16179692 ; 1305)

Edition	1st ed. 1988.
Publisher	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Year	1988
Size	VIII, 156 p : online resource
Authors	*Lubinsky, Doron S author Saff, Edward B author SpringerLink (Online service)
Subjects	LCSH:Numerical analysis FREE:Numerical Analysis
Notes	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 0. The results are consequences of a strengthened form of the following assertion: Given 0 <p<, f Lp ( ) and a certain sequence of positive numbers associated with Q(x), there exist polynomials Pn of degree at most n, n = 1,2,3..., such that if and only if f(x) = 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 HTTP:URL=https://doi.org/10.1007/BFb0082413

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