Asymptotic distribution of resonances for convex obstacles
type: Item
instance of: scholarly article
title: Asymptotic distribution of resonances for convex obstacles
zbMATH Open document ID: 0989.35099
DOI: 10.1007/BF02392828
author: Maciej Zworski
author: Johannes Sjöstrand
published in: Acta Mathematica
publication date: 2000-12-06T00:00:00Z
review text: The paper deals with the subject of locating and estimating resonances for convex bodies. It continues authors' previous work on upper bounds on the number of resonances in neighbourhoods of the real axis. The authors turn resonances into eigenvalues of a nonselfadjoint operator, proceed to a second microlocal reduction of the scaled problem to the boundary and establish a trace formula for the reduced problem.
Mathematics Subject Classification ID: 35P20
Mathematics Subject Classification ID: 35A27
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 58J37
Mathematics Subject Classification ID: 81U05
zbMATH DE Number: 1541215
zbMATH Keywords: asymptotic analysis
zbMATH Keywords: trace formula
reviewed by: Dumitru Motreanu
MaRDI profile type: Publication
Wikidata QID: Q56812808
cites work: The analytic extension of the resolvent of outer three-dimensional problems for Laplace operators in the second sheet
cites work: Scattering frequencies and Gevrey 3 singularities
cites work: Q4264393
cites work: Rigorous justification of the asymptotic solutions of ''sliding wave'' type
cites work: Scattering asymptotics for Riemann surfaces
cites work: Diffraction by a convex obstacle
cites work: Résonances en limite semi-classique
cites work: Q3736112
cites work: Decaying modes for the wave equation in the exterior of an obstacle
cites work: FBI transforms in Gevrey classes
cites work: Deuxième microlocalisation sur les sous variétés isotropes
cites work: Q4896037
cites work: Q3756685
cites work: Q3029422
cites work: Autour de l'approximation semi-classique. (Around semiclassical approximation)
cites work: Geometric bounds on the density of resonances for semiclassical problems
cites work: Density of Resonances for Strictly Convex Analytic Obstacles
cites work: Complex Scaling and the Distribution of Scattering Poles
cites work: Lower bounds on the number of scattering poles
cites work: Lower bounds on the number of scattering poles. II
cites work: Estimates on the number of scattering poles near the real axis for strictly convex obstacles
cites work: The complex scaling method for scattering by strictly convex obstacles
cites work: Quasimodes and resonances: sharp lower bounds
cites work: From quasimodes to resonances
cites work: Sharp bounds on the number of scattering poles in even-dimensional spaces
cites work: Q4310192
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description: scientific article; zbMATH DE number 1541215