Asymptotics on the number of scattering poles for degenerate perturbations of the Laplacian
type: Item
instance of: scholarly article
title: Asymptotics on the number of scattering poles for degenerate perturbations of the Laplacian
zbMATH Open document ID: 0862.35082
published in: Journal of Functional Analysis
publication date: 1997-05-26T00:00:00Z
review text: The author obtains an asymptotic on the number of scattering poles (or resonances) of compactly supported hypoelliptic perturbations of \(-\Delta\) in \(\mathbb{R}^n\), \(n\geq 3\), odd. By results of \textit{J. Sjöstrand} and \textit{M. Zworski} [Commun. Partial Differ. Equations 17, No. 5/6, 1021-1035 (1992; Zbl 0766.35031), J. Funct. Anal. 123, No. 2, 336-367 (1994; Zbl 0823.35137)] the problem is reduced to prove an asymptotic on the number of eigenvalues of the corresponding reference operator. Thus, many results of the author on upper bounds of the number of scattering poles for such perturbations are improved.
reviewed by: Karl Heinz Jansen
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 35P20
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 47A40
zbMATH DE Number: 908028
zbMATH Keywords: hypoelliptic perturbations
zbMATH Keywords: asymptotic on the number of eigenvalues
author: Georgi Vodev
MaRDI profile type: Publication
full work available at URL: jfan.1996.0066
OpenAlex ID: W2022538798
DOI: 10.1006/JFAN.1996.0066
description: scientific article; zbMATH DE number 908028