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Parametrices and dispersive estimates for Schrödinger operators with variable coefficients

From: American Journal of Mathematics
Volume 130, Number 3, June 2008
pp. 571-634 | 10.1353/ajm.0.0000

Abstract

Abstract:

In this article we consider variable coefficient time dependent Schr\"odinger evolutions in ${\Bbb R}^n$. Using phase space methods we construct outgoing parametrices and prove Strichartz type estimates globally in time. This is done in the context of $C^2$ metrics which satisfy a weak asymptotic flatness condition at infinity.



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