Trace estimates and improved pointwise bounds for joint eigenfunctions
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913058940518400 |
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| author | Wu, Xianchao Xiao, Xiao |
| author_facet | Wu, Xianchao Xiao, Xiao |
| contents | For $L^2$-normalized joint eigenfunctions in a quantum integrable system, [GT20] gave polynomial improvements over the standard Hömander 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22197 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Trace estimates and improved pointwise bounds for joint eigenfunctions Wu, Xianchao Xiao, Xiao Analysis of PDEs Mathematical Physics Spectral Theory For $L^2$-normalized joint eigenfunctions in a quantum integrable system, [GT20] gave polynomial improvements over the standard Hömander 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. |
| title | Trace estimates and improved pointwise bounds for joint eigenfunctions |
| topic | Analysis of PDEs Mathematical Physics Spectral Theory |
| url | https://arxiv.org/abs/2604.22197 |