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Zolotarevω-Polynomials inWrHω[0, 1]

✍ Scribed by Sergey K. Bagdasarov

Book ID
102969302
Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
519 KB
Volume
90
Category
Article
ISSN
0021-9045

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✦ Synopsis

The main result of this paper characterizes generalizations of Zolotarev polynomials as extremal functions in the Kolmogorov Landau problem

C ) where |(t) is a concave modulus of continuity, r, m: 1 m r, are integers, and B B 0 (r, m, |). We show that the extremal functions Z B have r+1 points of alternance and the full modulus of continuity of Z (r) B : |(Z (r) B ; t)=|(t) for all t # [0, 1]. This generalizes the Karlin's result on the extremality of classical Zolotarev polynomials in the problem (C) for |(t)=t and all B B r . 1997 Academic Press Let L r :=&C r & C [0, 1] =2 &2r&1 Â(r+1)! By (0.2), [T i = 1 2 (1+cos(?iÂ(r+1)))] r+1 i=0 article no. AT963086 340

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