Absence of positive eigenvalues of magnetic Schrodinger operators

We study sufficient conditions for the absence of positive eigenvalues of magnetic Schrodinger operators in R-d, d >= 2. 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. As applications, we describe several consequences of the main result for two-dimensional Pauli and Dirac operators, and two and three dimensional Aharonov-Bohm operators.