Resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds I: Resolvent construction at high energy

Abstract

ABSTRACTABSTRACTThis is the first in a series of papers in which we investigate the resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds with applications to the restriction theorem, spectral multiplier results and Strichartz estimates. In this first paper, we construct the high energy resolvent on general non-trapping asymptotically hyperbolic manifolds, using semiclassical Lagrangian distributions and semiclassical intersecting Lagrangian distributions, together with the 0-calculus of Mazzeo-Melrose.Our results generalize recent work of Melrose, Sá Barreto and Vasy, which applies to metrics close to the exact hyperbolic metric. We note that there is an independent work by Y. Wang which also constructs the high-energy resolvent.KEYWORDS: Asymptotically hyperbolic manifoldsfourier integral operatorintersecting Lagrangian distributionresolventsemiclassical analysis2010 MATHEMATICS SUBJECT CLASSIFICATION: 58J4058J50 AcknowledgmentsThe authors would like to thank C. Guillarmou, F. Rochon and A. Vasy for various helpful discussions while working on this paper.

Locations

• Communications in Partial Differential Equations - View
• arXiv (Cornell University) - View - PDF