Estimate of the Norm of the Hermite—Fejér Interpolation Operator in Sobolev Spaces

Resumo

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.