FBI transforms in Gevrey classes
type: Item
instance of: scholarly article
title: FBI transforms in Gevrey classes
zbMATH Open document ID: 0898.35069
DOI: 10.1007/BF02843155
author: Bernard Lascar
author: Richard Lascar
published in: Journal d'Analyse Mathématique
publication date: 1998-10-13T00:00:00Z
review text: The following theorem is proved: Let \({\mathcal O}\) be a Gevrey \(s\) strictly convex obstacle, \(1 \leq s < 3\). Then for every positive \(\varepsilon\) there are only finitely many resonances in the region \(\{ k \in {\mathbb C} \mid\text{Re }k \geq 1, \text{ Im } k \geq -(C_{0, a} - \varepsilon) (\text{Re } k)^{1/3} \}\). Here \(C_{0, a}\) is the constant found in a preceding paper by J. Sjöstrand. To prove such a result they develop a suitable Gevrey class FBI machinery, which will very likely be useful for other future applications.
reviewed by: Antonio Bove
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 35P05
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 1146575
zbMATH Keywords: number of resonances
zbMATH Keywords: convex obstacle
MaRDI profile type: Publication
cites work: Scattering frequencies and Gevrey 3 singularities
cites work: On Universal Moment Problems.
cites work: Diffraction by a convex obstacle
cites work: Differential Topology
cites work: Q3671564
cites work: Propagation des Singularites Gevery pour des Operateurs Hyperboliques
cites work: Propagation des singularites gevrey pour des problemes aux limites hyperboliques
cites work: Propagation des singularites Gevrey pourla diffraction
cites work: Q4063944
cites work: Density of Resonances for Strictly Convex Analytic Obstacles
cites work: Q3037865
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
description: scientific article; zbMATH DE number 1146575