Weighted Lp Error of Lagrange Interpolation
نویسندگان
چکیده
منابع مشابه
Complex interpolation of weighted noncommutative Lp-spaces
Let M be a semifinite von Neumann algebra equipped with a semifinite normal faithful trace τ . Let d be an injective positive measurable operator with respect to (M, τ ) such that d is also measurable. Define Lp(d) = {x ∈ L0(M) : dx+ xd ∈ Lp(M)} and ‖x‖Lp(d) = ‖dx+ xd‖p . We show that for 1 6 p0 < p1 6 ∞, 0 < θ < 1 and α0 > 0, α1 > 0 the interpolation equality (Lp0(d 0), Lp1(d α))θ = Lp(d ) hol...
متن کاملExtended Lagrange interpolation in weighted uniform norm
The author studies the uniform convergence of extended Lagrange interpolation processes based on the zeros of Generalized Laguerre polynomials. 2009 Elsevier Inc. All rights reserved.
متن کاملVector-valued Lp-convergence of orthogonal Lagrange Interpolation
Vector-valued L p-convergence of orthogonal series and Lagrange interpolation. Abstract We give necessary and sufficient conditions for interpolation inequalities of the type considered by Marcinkiewicz and Zygmund to be true in the case of Banach space-valued polynomials and Jacobi weights and nodes. We also study the vector-valued expansion problem of L p-functions in terms of Jacobi polynomi...
متن کاملOn the Lebesgue Function of Weighted Lagrange Interpolation. Ii
The aim of this paper is to continue our investigation of the Lebesgue function of weighted Lagrange interpolation by considering Erdős weights on R and weights on [ 1;1]. The main results give lower bounds for the Lebesgue function on large subsets of the relevant domains. 1991 Mathematics subject classification (Amer. Math. Soc.): 41A05, 41A10.
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 ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1995
ISSN: 0021-9045
DOI: 10.1006/jath.1995.1082