What is Jackson's constant?
arXiv:2607.23375
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.
arXiv comment7 pages, incorporated revisions, accepted by Applied Mathematics Letters