Bernstein and Kantorovich polynomials diminish the $\Lambda$-variation
Functional Analysis
2017-03-07 v2
Abstract
We prove the -variation diminishing property of the Bernstein and Kantorovich polynomials. Next we apply this result to characterize the space as the closure of the space of polynomials in the norm. A new proof of the separability of is given.
Cite
@article{arxiv.1609.00973,
title = {Bernstein and Kantorovich polynomials diminish the $\Lambda$-variation},
author = {Klaudiusz Czudek},
journal= {arXiv preprint arXiv:1609.00973},
year = {2017}
}
Comments
15 pages; corrected typos, reformulated argument before Observation 1, reformulated Theorem 7, results unchanged