Polynomial bounds on the number of resonances for some complete spaces of constant negative curvature near infinity
Polynomial bounds on the number of resonances for some complete spaces of constant negative curvature near infinity
复制标题
对于一些接近无穷大的恒定负曲率的完整空间，共振数的多项式界限
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
M. Zworski
中科院分区：
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作者：
Laurent Guillopé;M. Zworski
吉洛普湖和m.张文，常负曲率完备空间的共振数的多项式界，渐近分析，1995年，第11期，第1 - 22页。设X是共形紧的n维流形，在无穷远处具有常负曲率。X上拉普拉斯算子的预解式（ilsCn 1 s> 1，Re s> n 1）推广到C上的亚纯算子族，其极点称为共振极点或散射极点.如果NxCr）是半径为r的圆盘中的共振数，则我们证明以下上界：NxCr）：（Crn +! + C.
Guillope,L. and M. Zworski, Polynomial bounds on the number of resonances for some complete spaces of constant negative curvature near infinity, Asymptotic Analysis 11 (1995) 1-22. Let X be a conforrnally compact n-dimensional manifold with constant negative curvature -1 near infinity. The resolvent (ilsCn 1 s»-I, Re s > n 1, of the Laplacian on X extends to a meromorphic family of operators on C and its poles are called resonances or scattering poles. If NxCr) is the number of resonances in a disc of radius r we prove the following upper bound: NxCr) :( Crn+! + C.