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Complex interpolating polynomials

Author: A. K. Varma
Journal: Proc. Amer. Math. Soc. 103 (1988), 125-130
MSC: Primary 30E05; Secondary 41A05
MathSciNet review: 938655
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Abstract: Let $ {I_{n,m}}\left( {f,z} \right)$ be the unique interpolatory polynomial of degree $ \leq 2n - 1$ satisfying the conditions given by (1.1) where the $ {z_{kn}}$'s are the zeros of the polynomial $ {z^n} - 1$. The object of this paper is to consider the rate of convergence of $ {I_{m,n}}\left( {f,z} \right)$ to $ f\left( z \right)$ in the $ {L_p}$ norm where $ f \in C\left[ {\vert z\vert \leq 1} \right]$. This problem was initially raised by P. Turán in the case $ p = 2$ and in this case the solution was obtained by J. Szabados and A. K. Varma in [7].

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