SPECTRUM OF 3-DIMENSIONAL LANDAU OPERATOR PERTURBED BY A PERIODIC POINT POTENTIAL

A study is made of a three-dimensional Schrodinger operator with magne tic field and perturbed by a periodic sum of zero-range potentials. In the case of a rational flux, the explicit form of the decomposition o f the resolvent of this operator with respect to the spectrum of irred ucible representations of the group of magnetic translations is found. In the case of integer flux, the explicit form of the dispersion laws is found, the spectrum is described, and a qualitative investigation of it is made (in particular, it is established that not more than one gap exists).