Geodesic
Estimate of the Norm of the Hermite--Fej\'er Interpolation Operator in Sobolev Spaces
Matematičeskie zametki, Tome 105 (2019) no. 6, pp. 911-925

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Upper bounds for the norms of Hermite–Fejér interpolation operators in one-dimensional and multidimensional periodic Sobolev spaces are obtained. It is shown that, in the one-dimensional case, the norm of this operator is bounded. In the multidimensional case, the upper bound depends on the ratio of the numbers of nodes on separate coordinates.
Keywords: Hermite–Fejér interpolation operator
Mots-clés : Sobolev spaces. 
@article{MZM_2019_105_6_a8,
     author = {A. I. Fedotov},
     title = {Estimate of the {Norm} of the {Hermite--Fej\'er} {Interpolation} {Operator} in {Sobolev} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {911--925},
     publisher = {mathdoc},
     volume = {105},
     number = {6},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_105_6_a8/}
}
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A. I. Fedotov. Estimate of the Norm of the Hermite--Fej\'er Interpolation Operator in Sobolev Spaces. Matematičeskie zametki, Tome 105 (2019) no. 6, pp. 911-925. http://geodesic.mathdoc.fr/item/MZM_2019_105_6_a8/