Precise informations on the poles of the scattering matrix for two strictly convex obstacles

作者：Mitsuru Ikawa · 发表于：Kyoto journal of mathematics · 年份：1987 · DOI：10.1215/kjm/1250520765 · 被引用次数：16 · 研究领域：Electromagnetic Scattering and Analysis、Numerical methods in inverse problems、Matrix Theory and Algorithms

Precise informations on the poles of the scattering matrix for two strictly convex obstacles ByMitSUrli IKAWA 1. Introduction.In the previous papers [3, 4] we considered the scattering matrix for two strictly convex obstacles.To say more precisely, let 0 i , j= 1 , 2 , be bounded and strictly convex open sets in R 3 with smooth boundary3 a 2 where d = E " Denote by Y'(z) the scattering matrix for this problem.About j= i O X 1 the definition of the scattering matrix see for example Lax and Phillips [7, page 9].We showed in [3, 4] the following facts: (i) There exist positive constants c o and c, such that for any e>0contains only a finite number of poles of 5"(z), where(ii) For large Ij , B i contains at least one pole.The purpose of this paper is to give very precise informations on the poles in B .Namely, we shall show the following Theorem 1.For large I il (a) every B i contains exactly one pole of 9'(z), Communicated by Prof. S. Mizohata,