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arXiv · 2604.22197

Trace estimates and improved pointwise bounds for joint eigenfunctions

Xianchao Wu·Xiao Xiao
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Abstract

For $L^2$-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 $h^{\frac{-n+k+1}2}$ for the points satisfying a rank $k$ non-degeneracy condition.

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Xianchao Wu, Xiao Xiao. 2026-04-24. Trace estimates and improved pointwise bounds for joint eigenfunctions. https://arxiv.org/abs/2604.22197

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