An upper bound for the norm of the Chebyshev polynomial on two intervals

Publikation: Beitrag in FachzeitschriftArtikelBegutachtung

10 Zitate (Scopus)

Abstract

Let E:=[−1,α]∪[β,1], −1<α<β<1, be the union of two real intervals and consider the Chebyshev polynomial of degree n on E, that is, that monic polynomial which is minimal with respect to the supremum norm on E. For its norm, called the n-th Chebyshev number of E, an upper bound in terms of elementary functions of α and β is given. The proof is based on results of N.I. Achieser in the 1930s in which the norm is estimated with the help of Zolotarev's transformation using Jacobi's elliptic and theta functions.

OriginalspracheEnglisch
Seiten (von - bis)871-883
Seitenumfang13
FachzeitschriftJournal of Mathematical Analysis and Applications
Jahrgang445
Ausgabenummer1
DOIs
PublikationsstatusVeröffentlicht - 1 Jän. 2017

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