论文标题
各向异性Shubin操作员的光谱不平等现象
Spectral Inequalities For Anisotropic Shubin Operators
论文作者
论文摘要
在本文中，介绍了各向异性舒宾算子的特征函数有限组合的新光谱不平等。给定子集$ω$和一个能级，我们对L 2（r d）纳态的比率明确控制了L 2（$ω$） - 相对于能级的标准。这些证明是基于Gelfand-Shilov空间中的最新不确定性原理和Paul Alphonse证明的定量平滑效应推导出的伯恩斯坦类型估计。这些频谱不平等允许在任何控制子集中得出无效的可控制性，除了谐波振荡器外，与各向异性Shubin oberator相关的积极lebesgue量度测量了与各向异性Shubin运算符相关的进化方程。
In this paper, new spectral inequalities for finite combinations of eigenfunctions of anisotropic Shubin operators are presented. Given a subset $ω$ and an energy level, we provide an explicit control of the ratio of the L 2 (R d)-norm over the L 2 ($ω$)-norm with respect to the energy level. The proofs are based on recent uncertainty principles holding in Gelfand-Shilov spaces and Bernstein type estimates deduced from quantitative smoothing effects proved by Paul Alphonse. These spectral inequalities allow to derive the null-controllability in any positive time from any control subset with positive Lebesgue measure of evolution equations associated to anisotropic Shubin operators, except for the harmonic oscillator.
