Resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds I: Resolvent construction at high energy
Resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds I: Resolvent construction at high energy
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DOI：
10.1080/03605302.2015.1116561
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发表时间：
2014-10
影响因子：
1.9
通讯作者：
Xi Chen;Andrew Hassell
中科院分区：
文献类型：
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作者：
Xi Chen;Andrew Hassell
本文是一系列研究非陷渐近双曲流形的预解和谱测度的第一篇，并应用于限制定理、谱乘子结果和Strichartz估计。在第一篇文章中，我们利用半经典拉格朗日分布和半经典相交拉格朗日分布，以及Mazzeo-Melrose的0演算，构造了一般非陷于渐近双曲流形上的高能预解。我们的结果推广了梅尔罗斯、S·巴雷托和维希最近的工作，这些工作适用于接近精确双曲度量的度量。我们注意到有一项由Y.Wang独立完成的工作，它也构建了高能解析剂。
ABSTRACT This 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.