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A Trace Formula and Review of Some Estimates for Resonances

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Microlocal Analysis and Spectral Theory

Part of the book series: NATO ASI Series ((ASIC,volume 490))

Abstract

The main part of theses notes from the NATO ASI on microlocal analysis and spectral theory at Ti Ciocco, Sept.-Oct. 1996, is devoted to a new trace formula for resonances, which is valid for long range perturbations of the Laplacian in all dimensions. We work in the frame work of complex scaling and have a natural opportunity to review that method. We also review some lower bounds and some upper bounds on the density of resonances near the real axis, mainly following joint works with M.Zworski. The lower bounds however, are new in the case of even dimensions and form a first application of the new trace formula.

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Author information

Authors and Affiliations

  1. Centre de Mathématiques, Ecole Polytechnique, F-91128, Palaiseau, France

    J. Sjöstrand

  2. UA 169 CNRS, France

    J. Sjöstrand

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  1. J. Sjöstrand
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Editors and Affiliations

  1. Department of Mathematics, University of Torino, Torino, Italy

    Luigi Rodino

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© 1997 Springer Science+Business Media Dordrecht

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Sjöstrand, J. (1997). A Trace Formula and Review of Some Estimates for Resonances. In: Rodino, L. (eds) Microlocal Analysis and Spectral Theory. NATO ASI Series, vol 490. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5626-4_12

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  • DOI: https://doi.org/10.1007/978-94-011-5626-4_12

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6371-5

  • Online ISBN: 978-94-011-5626-4

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