On an Interpolation Process of Lagrange–hermite Type
نویسندگان
چکیده
Abstract. We consider a Lagrange–Hermite polynomial, interpolating a function at the Jacobi zeros and, with its first (r−1) derivatives, at the points ±1. We give necessary and sufficient conditions on the weights for the uniform boundedness of the related operator in certain suitable weighted L-spaces, 1 < p < ∞, proving a Marcinkiewicz inequality involving the derivative of the polynomial at ±1. Moreover, we give optimal estimates for the error of this process also in the weighted uniform metric.
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تاریخ انتشار 2012