Generalization of the Schwarz reflection principle in scattering theory for dissipative systems: application to purely imaginary resonant frequencies
Generalization of the Schwarz reflection principle in scattering theory for dissipative systems: application to purely imaginary resonant frequencies
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耗散系统散射理论中施瓦茨反射原理的推广：应用于纯虚部谐振频率
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发表时间：
1999
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通讯作者：
C. Labreuche
中科院分区：
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作者：
C. Labreuche
本文的目的是给出阻抗边界条件下纯虚轴上谐振频率个数计数函数的渐近估计。本文推广了P.Lax，R.菲利普斯和J.比尔谁研究了狄利克雷，诺依曼，罗宾边界条件与亥姆霍兹方程。他们开发的方法取决于散射矩阵的极点之间的特殊联系（即，谐振频率）和散射矩阵的零点。这个关系式对保守边界条件成立，但对吸收边界条件不成立。本文的第一部分是在寻找这种形式的阻抗边界条件的关系。然后我们遵循P.Lax，R.菲利普斯和J.比尔，以获得最终的估计。
The purpose of this paper is to give an asymptotic estimate of the counting function of the number of resonant frequencies on the purely imaginary axis in the case of the impedance boundary condition. We extend the work of P. Lax, R. Phillips, and J. Beale who studied the Dirichlet, Neumann, and Robin boundary conditions associated with the Helmholtz equation. The method they developed hinges on a special link between the poles of the scattering matrix (i.e., the resonant frequencies) and the zeros of the scattering matrix. This relation holds for conservative boundary conditions but not for absorbing boundary conditions. The first part of this paper consists in finding a relation of this form for the impedance boundary condition. Then we follow the work of P. Lax, R. Phillips, and J. Beale in order to get the final estimate.