English

Bernstein and Kantorovich polynomials diminish the $\Lambda$-variation

Functional Analysis 2017-03-07 v2

Abstract

We prove the Λ\Lambda-variation diminishing property of the Bernstein and Kantorovich polynomials. Next we apply this result to characterize the space CΛBVcC\Lambda BV_c as the closure of the space of polynomials in the ΛBV\Lambda BV norm. A new proof of the separability of CΛBVcC\Lambda BV_c 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

R2 v1 2026-06-22T15:39:37.784Z