Vol. 2, No. 1, 2009

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 6, 1285–1538
Issue 5, 1017–1284
Issue 4, 757–1015
Issue 3, 513–756
Issue 2, 253–512
Issue 1, 1–252

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
Cover
About the Cover
Editorial Board
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Resonances for nonanalytic potentials

André Martinez, Thierry Ramond and Johannes Sjöstrand

Vol. 2 (2009), No. 1, 29–60
Abstract

We consider semiclassical Schrödinger operators on n, with C potentials decaying polynomially at infinity. The usual theories of resonances do not apply in such a nonanalytic framework. Here, under some additional conditions, we show that resonances are invariantly defined up to any power of their imaginary part. The theory is based on resolvent estimates for families of approximating distorted operators with potentials that are holomorphic in narrow complex sectors around n.

Keywords
resonances, Schroedinger operators, Breit–Wigner peaks
Mathematical Subject Classification 2000
Primary: 35B34, 35P99, 47A10, 81Q20
Milestones
Received: 11 May 2008
Revised: 18 December 2008
Accepted: 11 January 2009
Published: 1 February 2009
Authors
André Martinez
Università di Bologna
Dipartimento di Matematica
Piazza di Porta San Donato 5
40127 Bologna
Italy
http://www.dm.unibo.it/~martinez/
Thierry Ramond
Département de Mathématiques
Université Paris-Sud 11
UMR CNRS 8628
91405 Orsay
France
http://www.math.u-psud.fr/~ramond
Johannes Sjöstrand
IMB (UMR CNRS 5584)
Université de Bourgogne
9 av. A. Savary
BP 47870
21078 Dijon Cedex
France