# American Institute of Mathematical Sciences

October  2007, 17(4): 771-786. doi: 10.3934/dcds.2007.17.771

## Smoothing-Strichartz estimates for the Schrodinger equation with small magnetic potential

 1 Department of Mathematics, University of Pisa, Pisa, Largo Bruno Pontecorvo 5, 56127, Italy, Italy 2 Department of Mathematics, University of Kansas, 1460 Jayhawk Blvd, Lawrence, KS 66045-7523, United States

Received  May 2006 Revised  October 2006 Published  January 2007

The work treats smoothing and dispersive properties of solutions to the Schrödinger equation with magnetic potential. Under suitable smallness assumption on the potential involving scale invariant norms we prove smoothing - Strichartz estimate for the corresponding Cauchy problem. An application that guarantees absence of pure point spectrum of the corresponding perturbed Laplace operator is discussed too.
Citation: Vladimir Georgiev, Atanas Stefanov, Mirko Tarulli. Smoothing-Strichartz estimates for the Schrodinger equation with small magnetic potential. Discrete & Continuous Dynamical Systems - A, 2007, 17 (4) : 771-786. doi: 10.3934/dcds.2007.17.771
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