Resolvent bounds for Lipschitz potentials in dimension two and higher with singularities at the origin
Donnell Obovu
University College London, London, UK
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Abstract
We consider, for , the semiclassical Schrödinger operator in dimension two and higher. The potential and its radial derivative are bounded away from the origin, have long-range decay and is bounded by near the origin while is bounded by , where . In this setting, we show that the resolvent bound is exponential in , while the exterior resolvent bound is linear in .
Cite this article
Donnell Obovu, Resolvent bounds for Lipschitz potentials in dimension two and higher with singularities at the origin. J. Spectr. Theory 14 (2024), no. 1, pp. 163–183
DOI 10.4171/JST/486