On mean convergence of Hermite–Fejér and Hermite interpolation for Erdős weights
نویسندگان
چکیده
منابع مشابه
Convergence of Hermite and Hermite-Fejér Interpolation of Higher Order for Freud Weights
We investigate weighted Lp(0 < p <.) convergence of Hermite and Hermite– Fejér interpolation polynomials of higher order at the zeros of Freud orthogonal polynomials on the real line. Our results cover as special cases Lagrange, Hermite– Fejér and Krylov–Stayermann interpolation polynomials. © 2001 Academic Press
متن کاملHermite and Hermite-fejér Interpolation of Higher Order and Associated Product Integration for Erdős Weights
Using the results on the coefficients of Hermite-Fejér interpolations in [5], we investigate convergence of Hermite and Hermite-Fejér interpolation of order m, m = 1, 2, . . . in Lp(0 < p < ∞) and associated product quadrature rules for a class of fast decaying even Erdős weights on the real line.
متن کاملMean convergence of Lagrange interpolation for Freud’s weights with application to product integration rules
The connection between convergence of product integration rules and mean convergence of Lagrange interpolation in L, (1 <p < 00) has been thoroughly analysed by Sloan and Smith [37]. Motivated by this connection, we investigate mean convergence of Lagrange interpolation at the zeros of orthogonal polynomials associated with Freud weights on R. Our results apply to the weights exp(-x”/2), m = 2,...
متن کاملOn Mean Convergence of Lagrange Interpolation for General Arrays
For n 1, let fxjngnj=1 be n distinct points in a compact set K R and let Ln[ ] denote the corresponding Lagrange Interpolation operator. Let v be a suitably restricted function on K. What conditions on the array fxjng1 j n; n 1 ensure the existence of p > 0 such that lim n!1 k (f Ln[f ]) v kLp(K)= 0 for every continuous f :: K ! R ? We show that it is necessary and su cient that there exists r ...
متن کاملOn Weighted Mean Convergence of Lagrange Interpolation for General Arrays
For n 1, let fxjngnj=1 be n distinct points and let Ln[ ] denote the corresponding Lagrange Interpolation operator. Let W : R ! [0;1). What conditions on the array fxjng1 j n; n 1 ensure the existence of p > 0 such that lim n!1 k (f Ln[f ])W b kLp(R)= 0 for every continuous f : R ! Rwith suitably restricted growth, and some weighting factor ? We obtain a necessary and su¢ cient condition for ...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2001
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(00)00698-1