Analytic Continuation and Semiclassical Resolvent Estimates on Asymptotically Hyperbolic Spaces

被引：18

作者：

Melrose, Richard ^{[1
]}

Barreto, Antonio Sa ^{[2
]}

Vasy, Andras ^{[3
]}

机构：

[1] MIT, Dept Math, Cambridge, MA 02139 USA

[2] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[3] Stanford Univ, Dept Math, Stanford, CA 94305 USA

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2014年 / 39卷 / 03期

基金：

美国国家科学基金会;

关键词：

Analytic continuation; Asymptotically hyperbolic spaces; High-energy resolvent estimates; Semiclassical parametrix construction; 58G25; 58J40; 35P25; WAVE-EQUATION; LOCAL ENERGY; RESONANCES; DECAY;

D O I：

10.1080/03605302.2013.866957

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we construct a parametrix for the high-energy asymptotics of the analytic continuation of the resolvent on a Riemannian manifold which is a small perturbation of the Poincare metric on hyperbolic space. As a result, we obtain non-trapping high energy estimates for this analytic continuation.

引用

页码：452 / 511

页数：60

共 24 条

[1]

[Anonymous], 2012, MSRI PUBLICATIONS

[2]

Barreto AS, 1997, MATH RES LETT, V4, P103

[3] Decay and non-decay of the local energy for the wave equation on the De Sitter-Schwarzschild metric [J].