On Weighted Mean Convergence of Lagrange Interpolation for General Arrays
نویسندگان
چکیده
منابع مشابه
On 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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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 ...
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Let Pd(C ) denote the space of polynomials of degree at most d in n complex variables. A subset X of C – we will usually speak of configuration or array – is said to be unisolvent for Pd(C ) (or simply unisolvent of degree d) if, for every function f defined on X there exists a unique polynomial P ∈ Pd(C ) such that P(x) = f (x) for every x ∈ X. This polynomial is called the Lagrange interpolat...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2002
ISSN: 0021-9045
DOI: 10.1006/jath.2002.3698