Abstract
We consider discrete versions of the de la Vallée-Poussin algebraic operator. We give a simple sufficient condition in order that such discrete operators interpolate, and in particular we study the case of the Bernstein-Szegő weights. Furthermore we obtain good error estimates in the cases of the sup-norm and L1-norm, which are critical cases for the classical Lagrange interpolation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. Chanillo and B. Muckenhoupt, Weak Type Estimates for Cèsaro Sums of Jacobi Polynomial Series. Mem. Amer. Math. Soc., 102, No. 487 (1993).
G. Criscuolo and G. Mastroianni, Fourier and Lagrange operators in some weighted Sobolov-type spaces, Acta Sci. Math. (Szeged), 60, (1995), 131-148.
O. Kis and J. Szabados, On some de la Vallée-Poussin type discrete linear operators, Acta Math. Hungar., 47 (1986), 239-260.
D. S. Lubinsky and V. Totik, Best weighted polynomial approximation via Jacobi expansions, Siam J. Math. Anal., 25 (1994), 555-570.
G. Mastroianni, Boundedness of Lagrange operator in some functional spaces. A survey, in Approximation Theory and Function Series (Budapest, 1995), Bolyai Soc. Math. Studies, 5, (1996), pp. 117-139.
G. Mastroianni and M. G. Russo, Weighted Marcinkiewicz inequalities and boundedness of the Lagrange operator, to appear in Recent Trends in Mathematical Analysis and Applications, edited by T. Rassias (1999).
P. Nevai, Orthogonal Polynomials, Mem. Amer. Math. Soc., No. 213 (1979).
J. Szabados, On an interpolatory analogon of the de la Vallée-Poussin means, Studia Sci. Math. Hungar., 9 (1974), 187-190.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Themistoclakis, W. Some Interpolating Operators of de la Vallée-Poussin Type. Acta Mathematica Hungarica 84, 221–235 (1999). https://doi.org/10.1023/A:1006637303487
Issue Date:
DOI: https://doi.org/10.1023/A:1006637303487