HRT counterexamples with exponential tails

John Jasper; Dustin G. Mixon

HRT counterexamples with exponential tails

泛函分析 2026-08-13 v1

作者: John Jasper , Dustin G. Mixon

摘要

We build on the recent breakthrough of Faulhuber, Petersen, van Velthoven, and Voigtlaender that disproved the HRT conjecture with a Schwartz function and a $12$ -point configuration. We give a human-readable treatment of their mechanism and find HRT counterexample functions with exponential (or faster) decay. By a result of Bownik and Speegle, this is the fastest possible decay for an HRT counterexample, up to a logarithmic factor in the exponent.

引用

@article{arxiv.2608.13539,
  title  = {HRT counterexamples with exponential tails},
  author = {John Jasper and Dustin G. Mixon},
  journal= {arXiv preprint arXiv:2608.13539},
  year   = {2026}
}