What is Jackson's constant?
Numerical Analysis
2026-07-25 v1
Abstract
We prove a refinement of Jackson's theorem on the approximation of Lipschitz functions by trigonometric polynomials. Our result precisely characterizes the leading error term associated with Jackson's construction. We do the same for a related construction commonly used in the kernel polynomial method for spectral density estimation, which is slightly better than Jackson's construction in this respect.
Cite
@article{arxiv.2607.23375,
title = {What is Jackson's constant?},
author = {Rikhav Shah and John Urschel and Nicholas West},
journal= {arXiv preprint arXiv:2607.23375},
year = {2026}
}
Comments
6 pages