In order to approximate continuous functions on [0 , +∞) , we consider a Lagrange–Hermite polynomial, interpolating a finite section of the function at the zeros of some orthogonal polynomials and, with its first (r- 1) derivatives, at the point 0. We give necessary and sufficient conditions on the weights for the uniform boundedness of the related operator. Moreover, we prove optimal estimates for the error of this process in the weighted Lp and uniform metric.
Lagrange--Hermite interpolation on the real semiaxis
Notarangelo I.;
2016-01-01
Abstract
In order to approximate continuous functions on [0 , +∞) , we consider a Lagrange–Hermite polynomial, interpolating a finite section of the function at the zeros of some orthogonal polynomials and, with its first (r- 1) derivatives, at the point 0. We give necessary and sufficient conditions on the weights for the uniform boundedness of the related operator. Moreover, we prove optimal estimates for the error of this process in the weighted Lp and uniform metric.
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