Estimates on the number of scattering poles near the real axis for strictly convex obstacles
type: Item
instance of: scholarly article
title: Estimates on the number of scattering poles near the real axis for strictly convex obstacles
zbMATH Open document ID: 0784.35073
author: Maciej Zworski
author: Johannes Sjöstrand
publication date: 1994-01-26T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75019
review text: For the Dirichlet Laplacian in the exterior of a strictly convex obstacle, we show that the number of scattering poles of modulus \(\leq r\) in a small angle \(\theta\) near the real axis, can be estimated by Const. \(\theta^{3/2}r^ n\) for \(r\) sufficiently large depending on \(\theta\). Here \(n\) is the dimension.
Mathematics Subject Classification ID: 35P20
Mathematics Subject Classification ID: 35S15
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 47A20
zbMATH DE Number: 490693
zbMATH Keywords: resonance
zbMATH Keywords: complex scaling
zbMATH Keywords: semiclassical problem
zbMATH Keywords: Dirichlet Laplacian
zbMATH Keywords: exterior of a strictly convex obstacle
zbMATH Keywords: scattering poles
MaRDI profile type: Publication
OpenAlex ID: W2322697448
cites work: Polynomial bound on the number of scattering poles
cites work: Q3756685
cites work: Autour de l'approximation semi-classique. (Around semiclassical approximation)
cites work: The asymptotic solution of linear differential equations of the second order for large values of a parameter
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: Sharp bounds on the number of scattering poles for perturbations of the Laplacian
DOI: 10.5802/AIF.1355
published in: Annales de l’institut Fourier
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description: scientific article; zbMATH DE number 490693