A SHARP LOWER BOUND FOR A RESONANCE-COUNTING FUNCTION IN EVEN DIMENSIONS

被引：0

作者：

Christiansen, T. J. ^{[1
]}

机构：

[1] Univ Missouri, Dept Math, 202 Math Sci Bldg, Columbia, MO 65211 USA

来源：

ANNALES DE L INSTITUT FOURIER | 2017年 / 67卷 / 02期

关键词：

scattering theory; resonance; obstacle; metric; SCATTERING POLES; POLYNOMIAL BOUNDS; CONVEX OBSTACLES; WAVE-EQUATION; NUMBER; LAPLACIAN; RESOLVENT; EXTERIOR; OPERATOR; TRACE;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper proves sharp lower bounds on a resonance-counting function for obstacle scattering in even-dimensional Euclidean space without a need for trapping assumptions. Similar lower bounds are proved for some other compactly supported perturbations of -Delta on R-d, for example, for the Laplacian for certain metric perturbations on Rd. The proof uses a Poisson formula for resonances, complementary to one proved by Zworski in even dimensions.

引用

页码：579 / 604

页数：26

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