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.
Cite this article
Kiril Datchev, Long Jin, Exponential lower resolvent bounds far away from trapped sets. J. Spectr. Theory 10 (2020), no. 2, pp. 617–649DOI 10.4171/JST/307