Skip Navigation


Applied Mathematics Research eXpress Advance Access originally published online on October 22, 2009
Applied Mathematics Research eXpress (2009) 2009:1-13, doi:10.1093/amrx/abp003 published on November 6, 2009
This Article
Right arrow Full Text Freely available
Right arrow FREE Full Text (PDF) Freely available
Right arrow All Versions of this Article:
2009/1/1-b    most recent
abp003v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow How to cite this article
Google Scholar
Right arrow Articles by Nonnenmacher, S.
Right arrow Articles by Zworski, M.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Semiclassical Resolvent Estimates in Chaotic Scattering

Stéphane Nonnenmacher1 and Maciej Zworski2

1 Institut de Physique Théorique, CEA/DSM/PhT, Unité de recherche associée au CNRS, 91191 Gif-sur-Yvette, France
2 Mathematics Department, University of California, Evans Hall, Berkeley, CA 94720, USA

Correspondence: Correspondence to be sent to: snonnenmacher{at}cea.fr

We prove resolvent estimates for semiclassical operators such as – h2 {Delta} + V(x) in scattering situations. Provided the set of trapped classical trajectories supports a chaotic flow and is sufficiently filamentary, the analytic continuation of the resolvent is bounded by h– M in a strip whose width is determined by a certain topological pressure associated with the classical flow. This polynomial estimate has applications to local smoothing in Schrödinger propagation and to energy decay of solutions to wave equations.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.