Lower estimates for linear operators with smooth range
Classical Analysis and ODEs
2017-06-05 v1
Abstract
We introduce a new method to prove lower estimates for the approximation error of general linear operators with smooth range in terms of classical moduli of smoothness and related -functionals. In addition, we explicitly show how to derive lower estimates for positive linear operators with smooth range and apply this result to classical approximation operators. We finish with some remarks on the eigenvalues of Schoenberg's spline operator.
Cite
@article{arxiv.1706.00669,
title = {Lower estimates for linear operators with smooth range},
author = {Johannes Nagler},
journal= {arXiv preprint arXiv:1706.00669},
year = {2017}
}