论文标题
具有功率增长潜力的Schrödinger操作员的传感器衰减密度的传感器集合的光谱不平等
Spectral inequality with sensor sets of decaying density for Schrödinger operators with power growth potentials
论文作者
论文摘要
我们证明了具有限制潜力的Schrödinger操作员，特别是Shubin型的频谱不平等（一种特定类型的不确定性关系）。允许传感器组呈指数衰减，在确切允许的衰减速率取决于电势。该证明使用卡尔曼估计值，定量加权$ l^2 $估计和$ h^1 $ - 浓度估算的插值不平等，所有这些都用于操作员的频谱子空间中的功能。
We prove a spectral inequality (a specific type of uncertainty relation) for Schrödinger operators with confinement potentials, in particular of Shubin-type. The sensor sets are allowed to decay exponentially, where the precise allowed decay rate depends on the potential. The proof uses an interpolation inequality derived by Carleman estimates, quantitative weighted $L^2$-estimates and an $H^1$-concentration estimate, all of them for functions in a spectral subspace of the operator.
