Strong asymptotics for extremal polynomials associated with weights on IR

D.S. Lubinsky, E.B. Saff

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.

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[目次]

  • 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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この本の情報

書名 Strong asymptotics for extremal polynomials associated with weights on IR
著作者等 Lubinsky, Doron Shaul
Saff, Edward B.
Lubinsky Doron S.
Lubinsky D S
シリーズ名 Lecture notes in mathematics
出版元 Springer-Verlag
刊行年月 c1988
ページ数 vii, 153 p.
大きさ 25 cm
ISBN 0387189580
3540189580
NCID BA03486296
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言語 英語
出版国 ドイツ
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