The complex scaling method for scattering by strictly convex obstacles
type: Item
instance of: scholarly article
title: The complex scaling method for scattering by strictly convex obstacles
zbMATH Open document ID: 0839.35095
DOI: 10.1007/BF02559608
author: Maciej Zworski
author: Johannes Sjöstrand
published in: Arkiv för Matematik
publication date: 1996-06-05T00:00:00Z
review text: The purpose of this paper is to obtain upper bounds for the number of scattering poles in varying neighborhoods of the real axis for scattering by strictly convex obstacles with \(C^\infty\) boundaries. The new estimates generalize earlier results on the poles in small conic neighborhoods of the real axis by the authors [Ann. Inst. Fourier 43, No. 3, 769-790 (1993; Zbl 0784.35073)] and include the recent result of \textit{T. Hargé} and \textit{G. Lebeau} [Invent. Math. 118, No. 1, 161-196 (1994; Zbl 0831.35121)]. The proof is based on an ingenious choice of the angle of scaling appearing in Hargé-Lebeau and on the development of a new semi-classical reduction to the boundary partly inspired by the paper of the first author [Duke Math. J. 60, No. 1, 1-57 (1990; Zbl 0702.35188)].
reviewed by: Bernard Helffer
Mathematics Subject Classification ID: 35P25
zbMATH DE Number: 792858
zbMATH Keywords: upper bounds for the number of scattering poles
MaRDI profile type: Publication
cites work: Scattering frequencies and Gevrey 3 singularities
cites work: Wave packets and fourier integral operators
cites work: Diffraction by a convex obstacle
cites work: Q3671564
cites work: Q4016478
cites work: Q5579836
cites work: Q3037865
cites work: Geometric bounds on the density of resonances for semiclassical problems
cites work: Complex Scaling and the Distribution of Scattering Poles
cites work: Distribution of scattering poles near the real axis
cites work: Lower bounds on the number of scattering poles
cites work: Estimates on the number of scattering poles near the real axis for strictly convex obstacles
cites work: Q3667246
full work available at URL: https://doi.org/10.1007/bf02559608
OpenAlex ID: W2028741263
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description: scientific article; zbMATH DE number 792858