Acta mathematica scientia,Series B ›› 1995, Vol. 15 ›› Issue (4): 474-476.

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ON SOME EXTREMAL PROPERTIES OF ALGEBRAIC POLYNOMIALS

Xie Siqing   

  1. 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

Abstract: Let Pn 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|Pn(x)|≤1.

Key words: Algebraic polynomial, Interpolation

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