PreprintarXiv licencearXiv
What is Jackson's constant?
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.
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BibTeX
@misc{shah2026what,
title = {{What is Jackson's constant?}},
author = {Rikhav Shah and John Urschel and Nicholas West},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.23375},
eprint = {2607.23375},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.23375},
}
RIS
TY - UNPB
TI - What is Jackson's constant?
AU - Rikhav Shah
AU - John Urschel
AU - Nicholas West
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2607.23375
UR - https://arxiv.org/abs/2607.23375
AB - 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.
ER -