Boundary spectral estimates for semiclassical Gevrey operators

Haoren Xiong

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arXiv · 2408.09098

Boundary spectral estimates for semiclassical Gevrey operators

Haoren Xiong

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Abstract

We obtain the spectral and resolvent estimates for semiclassical pseudodifferential operators with symbol of Gevrey-$s$ regularity, near the boundary of the range of the principal symbol. We prove that the boundary spectrum free region is of size ${\mathcal O}(h^{1-\frac{1}{s}})$ where the resolvent is at most fractional exponentially large in $h$, as the semiclassical parameter $h\to 0^+$. This is a natural Gevrey analogue of a result by N. Dencker, J. Sj{\"o}strand, and M. Zworski in the $C^{\infty}$ and analytic cases.

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Haoren Xiong. 2024-08-17. Boundary spectral estimates for semiclassical Gevrey operators. https://arxiv.org/abs/2408.09098

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