Semiclassical Resolvent Estimates for Schrödinger Operators with Coulomb Singularities |
| |
Authors: | François Castella Thierry Jecko Andreas Knauf |
| |
Institution: | 1. IRMAR & IRISA – Université de Rennes 1, Campus de Beaulieu, F-35042, Rennes Cedex, France 2. IRMAR – Université de Rennes 1, Campus de Beaulieu, F-35042, Rennes Cedex, France 3. Mathematisches Institut, Universit?t Erlangen-Nürnberg, Bismarckstr. 1 1/2, D-91054, Erlangen, Germany
|
| |
Abstract: | Consider the Schr?dinger operator with semiclassical parameter h, in the limit where h goes to zero. When the involved long-range potential is smooth, it is well known that the boundary values of the operator’s
resolvent at a positive energy λ are bounded by O(h
−1) if and only if the associated Hamilton flow is non-trapping at energy λ. In the present paper, we extend this result to
the case where the potential may possess Coulomb singularities. Since the Hamilton flow then is not complete in general, our
analysis requires the use of an appropriate regularization.
Submitted: March 19, 2007. Accepted: March 3, 2008. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|