  It is shown that the renormalizability of the zero-range interaction in the
two-dimensional space is always followed by the existence of a bound state,
which is not true for odd-dimensional spaces. A renormalization procedure is
defined and the exact retarded Green's function for electrons moving in two
dimensions and interacting with both crossed magnetic and electric fields and
an attractive zero-range interaction is constructed. Imaginary parts of poles
of this Green's function determine lifetimes of quasi-bound (resonance) states.
It is shown that for some particular parameters the stabilization against decay
occurs even for strong electric fields.
