ON SOME EXTREMAL PROPERTIES OF ALGEBRAIC POLYNOMIALS

数学物理学报(英文版) ›› 1995, Vol. 15 ›› Issue (4): 474-476.

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ON SOME EXTREMAL PROPERTIES OF ALGEBRAIC POLYNOMIALS

谢四清

Wuhan Iust. of Math. Sci., Academia Sinica, Wuhan 430071, China

收稿日期:1993-08-21 修回日期:1994-04-18 出版日期:1995-12-25 发布日期:1995-12-25

ON SOME EXTREMAL PROPERTIES OF ALGEBRAIC POLYNOMIALS

Xie Siqing

Wuhan Iust. of Math. Sci., Academia Sinica, Wuhan 430071, China

Received:1993-08-21 Revised:1994-04-18 Online:1995-12-25 Published:1995-12-25

摘要/Abstract

摘要： Let P_n be an algebraic polynomial of degree n with real coefficients. We study the extremal properties of the integral ∫_-1¹(P"_n(x)）²dx and ∫_-1¹(1-x²)(P"_n(x)²dx subject to the constraint max_-1≤x≤1|P_n(x)|≤1.

关键词: Algebraic polynomial, Interpolation

Abstract: Let P_n be an algebraic polynomial of degree n with real coefficients. We study the extremal properties of the integral ∫_-1¹(P"_n(x)）²dx and ∫_-1¹(1-x²)(P"_n(x)²dx subject to the constraint max_-1≤x≤1|P_n(x)|≤1.

Key words: Algebraic polynomial, Interpolation

谢四清. ON SOME EXTREMAL PROPERTIES OF ALGEBRAIC POLYNOMIALS[J]. 数学物理学报(英文版), 1995, 15(4): 474-476.

Xie Siqing. ON SOME EXTREMAL PROPERTIES OF ALGEBRAIC POLYNOMIALS[J]. Acta mathematica scientia,Series B, 1995, 15(4): 474-476.

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ON SOME EXTREMAL PROPERTIES OF ALGEBRAIC POLYNOMIALS

ON SOME EXTREMAL PROPERTIES OF ALGEBRAIC POLYNOMIALS

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