Abstract: We study sufficient conditions for the absence of positive eigenvalues of magnetic Schroedinger  operators in R^n. In our main result we prove the absence of eigenvalues above certain threshold energy which depends explicitly on the magnetic and electric field.  A comparison with the examples of Miller-Simon shows that our result is sharp as far as the decay of the magnetic field is concerned.
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The talk is based on a joint work with Silvana Avramska-Lukarska and Dirk Hundertmark.