Boundary spectral estimates for semiclassical Gevrey operators

2024/08/17 by Haoren Xiong, Xiong, Haoren
Mathematics · Computer Science · #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.2408.09098

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-(1)/(s)) where the resolvent is at most fractional exponentially large in h, as the semiclassical parameter h→ 0⁺. This is a natural Gevrey analogue of a result by N. Dencker, J. Sjöstrand, and M. Zworski in the C^∞ and analytic cases.

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