The scattering operator on asymptotically hyperbolic manifolds

被引：0

作者：

Barreto, Antonio Sa ^{[1
]}

Wang, Yiran ^{[2
,3
]}

机构：

[1] Purdue Univ, Dept Math, 150 North Univ St, W Lafayette, IN 47907 USA

[2] Univ Washington, Dept Math, Box 354350, Seattle, WA 98195 USA

[3] Hong Kong Univ Sci & Technol, Inst Adv Study, Kowloon, Lo Ka Chung Bldg,Lee Shau Kee Campus, Hong Kong, Peoples R China

来源：

JOURNAL OF SPECTRAL THEORY | 2019年 / 9卷 / 01期

关键词：

Asymptotically hyperbolic manifolds; radiation fields; scattering; scattering relation; wave equation; X-RAY TRANSFORM; INVERSE SCATTERING; LAPLACE OPERATOR; RESOLVENT; CONTINUATION; RIGIDITY; FIELDS;

D O I：

10.4171/JST/248

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain a formula for the Schwartz kernel of the scattering operator in terms of the Schwartz kernel of the forward fundamental solution of the wave operator on asymptotically hyperbolic manifolds. This formula is then used to show that the scattering operator is a Fourier integral operator that quantizes the scattering relation.

引用

页码：269 / 313

页数：45

共 60 条

[41] LAGRANGIAN INTERSECTION AND THE CAUCHY-PROBLEM [J].

MELROSE, RB ;

UHLMANN, GA .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1979, 32 (04) :483-519

[42] Analytic Continuation and Semiclassical Resolvent Estimates on Asymptotically Hyperbolic Spaces [J].

Melrose, Richard ;

Barreto, Antonio Sa ;

Vasy, Andras .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2014, 39 (03) :452-511

[43]

Melrose Richard B., 1995, STANFORD LECT

[44]

PERRY PA, 1989, J REINE ANGEW MATH, V398, P67

[45] THE LAPLACE OPERATOR ON A HYPERBOLIC MANIFOLD .1. SPECTRAL AND SCATTERING-THEORY [J].

PERRY, PA .

JOURNAL OF FUNCTIONAL ANALYSIS, 1987, 75 (01) :161-187

[46]

Pestov L, 2006, CONTEMP MATH, V412, P249

[47] Stability estimates for the X-ray transform of tensor fields and boundary rigidity [J].

Stefanov, P ;

Uhlmann, G .

DUKE MATHEMATICAL JOURNAL, 2004, 123 (03) :445-467

[48]

Stefanov P, 1998, MATH RES LETT, V5, P83

[49]

Stefanov P., 2008, Algebraic analysis of differential equations from microlocal analysis to exponential asymptotics, P275

[50] ON THE STABLE RECOVERY OF A METRIC FROM THE HYPERBOLIC DN MAP WITH INCOMPLETE DATA [J].

Stefanov, Plamen ;

Uhlmann, Gunther ;

Vasy, Andras .

INVERSE PROBLEMS AND IMAGING, 2016, 10 (04) :1141-1147

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