A Microlocal Analysis of the Lévy Generator with Conjugate Points

被引：0
|
作者：
Tully, Kevin [1 ]
机构：
[1] Univ Washington, Dept Math, Box 354350, Seattle, WA 98195 USA
来源：
JOURNAL OF GEOMETRIC ANALYSIS | 2024年 / 34卷 / 12期
基金：
美国国家科学基金会;
关键词：
Microlocal analysis; L & eacute; vy process; Conjugate points; Fourier integral operators; X-RAY TRANSFORM; LEVY FLIGHT;
D O I：
10.1007/s12220-024-01813-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We analyze the microlocal structure of the infinitesimal generator of a L & eacute;vy process on a closed Riemannian manifold when conjugate points are allowed. We show that if there are no singular conjugate pairs, then the infinitesimal generator is microlocally equal to a sum of pseudodifferential operators and Fourier integral operators. This provides a microlocal analogue of known results for the flat torus, the sphere, and Anosov manifolds.
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页数：25
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