论文标题
部分可观测时空混沌系统的无模型预测
Resolvent estimates for one-dimensional Schrödinger operators with complex potentials
论文作者
论文摘要
我们研究一维schrödinger运算符$ \ permatatorName {h} = - \ partial_x^2 + v $带有无界的复杂电位$ v $，并得出了分辨率标准的渐近估计，$ψ（λ）：= \ | （\ operatorName {h}-λ）^{ - 1} \ | $，as $ |λ| \ to +\ infty $，单独考虑\ operatorname {ran} v $和$λ\ in \ mathbb {r} _ +$中的$λ\。在每种情况下，我们的分析都会产生一个确切的领先订单项和明确的剩余$ψ（λ）$，我们表明这些估计值是最佳的。我们还讨论了主要结果的几个扩展，它们与Semigroup理论的某些方面的相互关系，并用示例说明了它们。
We study one-dimensional Schrödinger operators $\operatorname{H} = -\partial_x^2 + V$ with unbounded complex potentials $V$ and derive asymptotic estimates for the norm of the resolvent, $Ψ(λ) := \| (\operatorname{H} - λ)^{-1} \|$, as $|λ| \to +\infty$, separately considering $λ\in \operatorname{Ran} V$ and $λ\in \mathbb{R}_+$. In each case, our analysis yields an exact leading order term and an explicit remainder for $Ψ(λ)$ and we show these estimates to be optimal. We also discuss several extensions of the main results, their interrelation with some aspects of semigroup theory and illustrate them with examples.
