Geometric bounds on the density of resonances for semiclassical problems
type: Item
instance of: scholarly article
title: Geometric bounds on the density of resonances for semiclassical problems
zbMATH Open document ID: 0702.35188
DOI: 10.1215/S0012-7094-90-06001-6
author: Johannes Sjöstrand
published in: Duke Mathematical Journal
publication date: 1990-01-01T00:00:00Z
review text: The author gives upper bounds on the number of resonances in certain regions in the complex plane close to the real axis, for semi-classical operators \(like:-h^ 2\Delta +V(x)\) when h is small. A part of the results was announced in the Proc. of the VIII Latin American School of Mathematics (1986) [Lect. Notes Math. 1324, 286-292 (1988; Zbl 0674.35018)]. The resonances are defined using a microlocal version of the complex scaling due to the reviewer and the author [Mém. Soc. Math. Fr., Nouv. Sér. 24/25 (1986; Zbl 0631.35075)] and the results presented here are analogous to those by \textit{R. Melrose} [Journ. ``Equations Deriv. Partielles'', St. Jean-De Monts 1984, Conf. No.3, 8 p. (1984; Zbl 0621.35073)] in the context of the exterior problem.
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 35J10
zbMATH DE Number: 4150925
zbMATH Keywords: resonances
zbMATH Keywords: semi-classical operators
zbMATH Keywords: complex scaling
reviewed by: Bernard Helffer
MaRDI profile type: Publication
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full work available at URL: s0012-7094-90-06001-6
OpenAlex ID: W1906752274
description: scientific article; zbMATH DE number 4150925