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An extension of Fejér’s condition for Hermite interpolation. (English) Zbl 1276.42006

Summary: We study the Hermite interpolation problem with equally spaced nodes on the unit circle. We obtain new conditions for the derivatives in order that the Hermite interpolants uniformly converge to continuous functions. As a consequence we obtain some improvements in the case of the bounded interval.

MSC:

42A15 Trigonometric interpolation
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
26D20 Other analytical inequalities
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