English

Trace estimates and improved pointwise bounds for joint eigenfunctions

Analysis of PDEs 2026-04-27 v1 Mathematical Physics math.MP Spectral Theory

Abstract

For L2L^2-normalized joint eigenfunctions in a quantum integrable system, [GT20] gave polynomial improvements over the standard H\"omander bounds for typical points. In this paper, we improve their result by establishing a sharp bound of hn+k+12h^{\frac{-n+k+1}2} for the points satisfying a rank kk non-degeneracy condition.

Keywords

Cite

@article{arxiv.2604.22197,
  title  = {Trace estimates and improved pointwise bounds for joint eigenfunctions},
  author = {Xianchao Wu and Xiao Xiao},
  journal= {arXiv preprint arXiv:2604.22197},
  year   = {2026}
}

Comments

22 pages, 2 figures

R2 v1 2026-07-01T12:33:18.460Z