We give examples of semiclassical Schrödinger operators with exponentially large cutoff resolvent norms, even when the supports of the cutoff and potential are very far apart. The examples are radial, which allows us to analyze the resolvent kernel in detail using ordinary differential equation techniques. In particular,we identify a threshold spatial radius where the resolvent behavior changes. We apply these results to wave equations with radial wavespeed, identifying a corresponding threshold radius at which wave decay properties change.

中文翻译：

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远离陷阱集的指数下界

我们给出了具有极大截止临界解析度范数的半经典Schrödinger算符的示例，即使截止和势的支持相距甚远。这些示例是径向的，这使我们能够使用普通的微分方程技术来详细分析可分辨的内核。特别是，我们确定了分辨行为改变的阈值空间半径。我们将这些结果应用于具有径向波速的波动方程，从而确定波动衰减特性发生变化的相应阈值半径。