Ikawa, Mitsuru On the poles of the scattering matrix for two strictly convex obstacles. (English) Zbl 0561.35060 J. Math. Kyoto Univ. 23, 127-194 (1983). Denote by S(\(\sigma)\) the scattering matrix for the Dirichlet initial boundary value problem for the wave equation in the exterior domain \({\mathcal D}\) of an open, bounded set \({\mathcal O}\) with sufficiently smooth boundary \(\Gamma\). S(\(\sigma)\) is a unitary mapping from \(L_ 2(S^ 2)\) onto \(L_ 2(S^ 2)\) for any \(\sigma\in {\mathbb{R}}\) and determines the scattering obstacle uniquely. The author considers the question of relating geometrical properties of the obstacle \({\mathcal O}\) and the distribution of poles of the meromorphic operator family S(z), \(z\in {\mathbb{C}}\). The main result of the paper provides information of the position of singularities of the scattering matrix in a particular trapping case: \({\mathcal O}\) consists of two disjoint strictly convex obstacles. The result is based on a refinement of a parametrix construction used in previous work of the author. The proofs are given in detail. Reviewer: R.Picard Cited in 2 ReviewsCited in 22 Documents MSC: 35P25 Scattering theory for PDEs 35L05 Wave equation Keywords:trapping obstacle; scattering matrix; Dirichlet initial boundary value problem; wave equation; exterior domain; scattering obstacle; distribution of poles; singularities of the scattering matrix; parametrix × Cite Format Result Cite Review PDF Full Text: DOI