MMN-1345
On saturation effect for linear shape-preserving approximation in Sobolev spaces
Abstract
Paper shows that if a linear finite-dimensional operator defined in Sobolev space preserves $k$-monotonicity then the error of approximation of the operator does not decrease with the increase of smoothness of approximated functions.
In other words, there is saturation effect for linear finite-rank operators defined in Sobolev space and preserving $k$-monotonicity.
Vol. 16 (2015), No. 2, pp. 1191-1197
DOI: 10.18514/MMN.2015.1345