Geodesic
Estimate of the Norm of the Lagrange Interpolation Operator in the Multidimensional Weighted Sobolev Space
Matematičeskie zametki, Tome 99 (2016) no. 5, pp. 752-763

Voir la notice de l'article provenant de la source Math-Net.Ru

An estimate of the norm of the Lagrange interpolation operator in the multidimensional weighted Sobolev space is obtained. It is shown that, under a certain choice of the sequence of multi-indices, the interpolating polynomials converge to the interpolated function and the rate of convergence is of the order of the best approximation of this function by algebraic polynomials in this space.
Keywords: Lagrange interpolation operator, weighted Sobolev space, interpolating polynomials, approximation by algebraic polynomials, Chebyshev polynomials
Mots-clés : Fourier coefficients of a polynomial. 
@article{MZM_2016_99_5_a8,
     author = {A. I. Fedotov},
     title = {Estimate of the {Norm} of the {Lagrange} {Interpolation} {Operator} in the {Multidimensional} {Weighted} {Sobolev} {Space}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {752--763},
     publisher = {mathdoc},
     volume = {99},
     number = {5},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_99_5_a8/}
}
TY  - JOUR
AU  - A. I. Fedotov
TI  - Estimate of the Norm of the Lagrange Interpolation Operator in the Multidimensional Weighted Sobolev Space
JO  - Matematičeskie zametki
PY  - 2016
SP  - 752
EP  - 763
VL  - 99
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2016_99_5_a8/
LA  - ru
ID  - MZM_2016_99_5_a8
ER  - 
%0 Journal Article
%A A. I. Fedotov
%T Estimate of the Norm of the Lagrange Interpolation Operator in the Multidimensional Weighted Sobolev Space
%J Matematičeskie zametki
%D 2016
%P 752-763
%V 99
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2016_99_5_a8/
%G ru
%F MZM_2016_99_5_a8
A. I. Fedotov. Estimate of the Norm of the Lagrange Interpolation Operator in the Multidimensional Weighted Sobolev Space. Matematičeskie zametki, Tome 99 (2016) no. 5, pp. 752-763. http://geodesic.mathdoc.fr/item/MZM_2016_99_5_a8/