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Lebesgue constant estimation in multidimensional Sobolev space
Lobachevskii journal of mathematics, Tome 14 (2004), pp. 25-32
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The norm estimation of the Lagrange interpolation operator is obtained. It is shown that the rate of convergence of the interpolative polynomials depends on the choice of the sequence of multiindices and, for some sequences, is equal to the rate of the best approximation of the interpolated function. 
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     author = {A. I. Fedotov},
     title = {Lebesgue constant estimation in multidimensional {Sobolev} space},
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}
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A. I. Fedotov. Lebesgue constant estimation in multidimensional Sobolev space. Lobachevskii journal of mathematics, Tome 14 (2004), pp. 25-32. http://geodesic.mathdoc.fr/item/LJM_2004_14_a2/

[1] Fedotov A. I., “On the asymptotic convergence of the polynomial collocation method for singular integral equations and periodic pseudodifferential equations”, Archivum mathematicum, 1 (2002), 1–13 | MR | Zbl

[2] Taylor, M. E., Pseudodifferential operators, Princeton University Press, Princeton, 1981 | MR | Zbl