ՀՀ ԳԱԱ Տեղեկագիր: Մաթեմատիկա =Известия НАН Армении: Математика =Proceedings of the NAS Armenia: Mathematics

Chebyshev's extremal problems of polynomial grown in real normed spaces

Revesz, Sz. G. and Sarantopoulos, Y. (2001) Chebyshev's extremal problems of polynomial grown in real normed spaces. Հայաստանի ԳԱԱ Տեղեկագիր. Մաթեմատիկա, 36 (5). pp. 62-81. ISSN 00002-3043

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    Abstract

    Let K be a convex body in a real space X, and let p : X - IR be a polynomial of degree n bounded by 1 on K. Given x € X / K, how large can p(x) be? This classical question was raised and settled by P. Chebyshev for one variable real polynomials, bounded on intervals (the only one dimensional convex bodies) one and a half century ago. Rivlin and Shapiro [23] gave a generalization of this Chebyshev problem IR for strictly convex bodies, and Kroo and Schmidt [12] solved the problem in IR for arbitrary convex bodies. The paper solves Chebyshev estremal problem for normed spaces. In the course of proof we obtain some new auxiliary geometric results, connected to the generalized Minkowski fnctional on normed spaces. As shown by examples, the previous finite dimensional considerations and resuls can not be extended to infinite dimensional spaces.

    Item Type: Article
    Additional Information: Чебышевские экстремальные задачи полиномиального роста в вещественных нормированных пространствах / С. Г. Ревес, Я. Сарантопулос.
    Subjects: Q Science > QA Mathematics
    Divisions: UNSPECIFIED
    Depositing User: Bibliographic Department
    Date Deposited: 01 Oct 2012 15:50
    Last Modified: 03 Oct 2012 13:17
    URI: http://mathematics.asj-oa.am/id/eprint/469

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