Strong Asymptotics for Extremal Polynomials Associated With Weights on R

Lubinsky, Doron S.; Saff, Edward B.

ISBN 10: 3540189580 / ISBN 13: 9783540189589

Editore: Springer, 1988

Unread book in perfect condition. Codice articolo 5900623

Riassunto:

0. The results are consequences of a strengthened form of the following assertion: Given 0

<, 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.

Contenuti: 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.

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Titolo: Strong Asymptotics for Extremal Polynomials ...
Casa editrice: Springer
Data di pubblicazione: 1988
Legatura: Brossura
Condizione: As New