Note on the distribution of poles of the scattering matrix
type: Item
instance of: scholarly article
title: Note on the distribution of poles of the scattering matrix
zbMATH Open document ID: 0562.35065
DOI: 10.1016/0022-247X(84)90122-7
author: Vesselin Petkov
published in: Journal of Mathematical Analysis and Applications
publication date: 1984-01-01T00:00:00Z
review text: Let \(K\subset R^ n\) be a bounded domain with a smooth boundary. Let \(\lambda_ j\) be the poles of the resolvent kernel of the Dirichlet Laplacian in the exterior to K domain. Assume that K has at least one isolated multiple reflecting periodic ray. Under this assumption it is proved that for every \(\epsilon >0\) there exist \(\lambda_ j\) such that \(0<Im \lambda_ j<\epsilon \log | \lambda_ j|.\)
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 35L20
zbMATH DE Number: 3895540
zbMATH Keywords: poles of the S-matrix
zbMATH Keywords: resolvent kernel
zbMATH Keywords: Dirichlet Laplacian
zbMATH Keywords: reflecting periodic ray
reviewed by: A. G. Ramm
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3895540