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«ՀՀ ԳԱԱ Տեղեկագիր: Մաթեմատիկա»-ն լույս է տեսնում 1966 թվականից՝ տարին 6 անգամ։
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Title:
Chebyshev's extremal problems of polynomial growth in real normed spaces
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Creator:
Sz. G. Révész ; Y. Sarantopoulos
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Գլխավոր խմբ․՝ Մ․ Մ․ Ջրբաշյան (1966-1994) ; Ռ․ Վ․ Համբարձումյան (1994-2009) ; Ա․ Ա․ Սահակյան (2010-)
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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.
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Երևան
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ՀՀ ԳԱԱ Հիմնարար գիտական գրադարան