Semiclassical principal symbols and Gutzwiller's trace formula
type: Item
instance of: scholarly article
title: Semiclassical principal symbols and Gutzwiller's trace formula
zbMATH Open document ID: 0794.58046
DOI: 10.1016/0034-4877(92)90019-W
published in: Reports on Mathematical Physics
publication date: 1994-08-15T00:00:00Z
review text: The paper studies the semiclassical trace formula of Gutzwiller [proved by \textit{M. Gutzwiller}, J. Math. Phys. 12, 343-358 (1971)] for the asymptotic expansion of the spectral density for the Schrödinger operator. This formula is closely related to a theorem of \textit{J. J. Duistermaat} and \textit{V. W. Guillemin} [Invent. Math. 29, 39-79 (1975; Zbl 0307.35071)] on the spectral asymptotics of positive, first order, elliptic pseudo-differential operators on compact manifolds, but a rigorous proof has apparently been given only recently by \textit{T. Paul} and \textit{A. Uribe} [C. R. Acad. Sci., Paris, Sér. I 313, No. 5, 217-222 (1991; Zbl 0738.58046)] after preliminary work of Guillemin-Uribe and Brummelhuis-Uribe. The present paper gives a new proof of the result by a direct adaptation of the Fourier integral calculus to the semiclassical context.
reviewed by: Otto Liess
Mathematics Subject Classification ID: 58J50
zbMATH DE Number: 459126
zbMATH Keywords: semiclassical trace formula
author: Eckhard Meinrenken
MaRDI profile type: Publication
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full work available at URL: 0034-4877(92)90019-w
OpenAlex ID: W2042704729
description: scientific article; zbMATH DE number 459126