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Polynomial approximation on the sphere using scattered data
We consider the problem of approximately reconstructing a function f defined on the surface of the unit sphere in the Euclidean space ℝq +1 by using samples of f at scattered sites. A central role isExpand
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Interpolating polynomial wavelets on [−1,1]
TLDR
Algebraic polynomial interpolating scaling functions and wavelets are constructed by using the interpolation properties of de la Vallée Poussin kernels. Expand
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The boundedness of the Cauchy singular integral operator in weighted Besov type spaces with uniform norms
The mapping properties of the Cauchy singular integral operator with constant coefficients are studied in couples of spaces equipped with weighted uniform norms. Recently weighted Besov type spacesExpand
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Some Interpolating Operators of de la Vallée-Poussin Type
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 theExpand
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On the numerical solution of some nonlinear and nonlocal boundary value problems
TLDR
In this paper, we study the numerical solution of a special class of nonlocal nonlinear boundary value problems, which involve the integral of the unknown solution over the integration domain. Expand
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A numerical method for the generalized airfoil equation based on the de la Vallée Poussin interpolation
The authors consider the generalized airfoil equation in some weighted Holder-Zygmund spaces with uniform norms. Using a projection method based on the de la Vallee Poussin interpolation, theyExpand
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On the Solution of a Class of Nonlinear Systems Governed by an -Matrix
We consider a weakly nonlinear system of the form ( 𝐼 + 𝜑 ( 𝑥 ) 𝐴 ) 𝑥 = 𝑝 , where 𝜑 ( 𝑥 ) is a real function of the unknown vector 𝑥 , and ( 𝐼 + 𝜑 ( 𝑥 ) 𝐴 ) is an 𝑀 -matrix. We proposeExpand
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Generalized de la Vallée Poussin approximations on [−1, 1]
TLDR
A general approach to de la Vallée Poussin means is given and the resulting near best polynomial approximation is stated by developing simple sufficient conditions to guarantee that the Lebesgue constants are uniformly bounded. Expand
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Uniform approximation on [−1, 1] via discrete de la Vallée Poussin means
TLDR
We construct a class of discrete de la Vallée Poussin means, by approximating the Fourier coefficients with a Gauss–Jacobi quadrature rule. Expand
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Weighted L1 approximation on [-1, 1] via discrete de la Vallée Poussin means
TLDR
We consider some discrete approximation polynomials, namely discrete de la Vallee Poussin means, which have been recently deduced from certain delayed arithmetic means of the Fourier–Jacobi partial sums, in order to get a near–best approximation in suitable spaces of continuous functions equipped with the weighted uniform norm. Expand
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