On Extrapolation of Polynomials with Real Coefficients to the Complex Plane
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The problem of the greatest possible absolute value of the kth derivative of an algebraic polynomial of order n > k with real coefficients at a given point of the complex plane is considered. It is assumed that the polynomial is bounded by 1 on the interval [-1,1]. It is shown that the solution is attained for the polynomial κ · Tσ, where Tσ is one of the Zolotarev or Chebyshev polynomials and κ is a number.
Keywordsextrapolation alternance Zolotarev polynomial dual problem
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This work was supported by the Russian Foundation for Basic Research under grants 17-01-00649, 16-01-00295, and 17-01-00809.