The Aharonov-Bohm Solenoids in a Constant Magnetic Field

We study the spectral properties of a two-dimensional magnetic Schrödinger operator The magnetic field is given by where B > 0 is a constant, and the points are uniformly separated. We give an upper bound for the number of eigenvalues of H_N between two Landau levels or below the lowest Landau level, when N is finite. We prove the spectral localization of H_N near the spectrum of the single solenoid operator, when are far from each other, all the values are the same, and the boundary conditions at z_j are uniform. We determine the deficiency indices of the minimal operator and give a characterization of self-adjoint extensions of the minimal operator.submitted 28/05/04, accepted 23/07/04