  We consider 2- and 3-dimensional Schr\"odinger or generalized
Schr\"odinger-Pauli operators with the non-degenerating magnetic field in the
open domain under certain non-degeneracy assumptions we derive pointwise
spectral asymptotics. We also consider asymptotics of some related expressions
(see below). For all asymptotics loops rather than periodic trajectories play
important role.
