Vol. 9, No. 4, 2016
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Resonance free regions for nontrapping manifolds with cusps

Kiril Datchev
Vol. 9 (2016), No. 4, 907–953
DOI: 10.2140/apde.2016.9.907
Abstract

We prove resolvent estimates for nontrapping manifolds with cusps which imply the existence of arbitrarily wide resonance free strips, local smoothing for the Schrödinger equation, and resonant wave expansions. We obtain lossless limiting absorption and local smoothing estimates, but the estimates on the holomorphically continued resolvent exhibit losses. We prove that these estimates are optimal in certain respects.

Keywords
cusp, resonances, resolvent, scattering, waves
Mathematical Subject Classification 2010
Primary: 58J50
Milestones
Received: 16 December 2015
Accepted: 26 February 2016
Published: 3 July 2016
Authors
Kiril Datchev
Mathematics Department
Purdue University
150 N. University Street
West Lafayette, IN 47907
United States