Abstract

We consider a family of surfaces of revolution, each with a single periodic geodesic which is degenerately unstable. We prove a local smoothing estimate for solutions to the linear Schrödinger equation with a loss that depends on the degeneracy, and we construct explicit examples to show our estimate is saturated on a weak semiclassical time scale. As a byproduct of our proof, we obtain a cutoff resolvent estimate with a sharp polynomial loss.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1601-1632
Launched on MUSE
2013-11-27
Open Access
No
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