On Extrapolation of Polynomials with Real Coefficients to the Complex Planeстатья
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Дата последнего поиска статьи во внешних источниках: 8 декабря 2019 г.
Аннотация: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. 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.