English

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}
}

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6 pages