  Let H be the discrete 3-dimensional Heisenberg group with the standard
generators x, y, z. The element Delta of the group algebra for H of the form
Delta= (x+x^{-1}+y+y^{-1})/4 is called the Laplace operator.
  This operator can also be defined as transition operator for random walk on
the group.
  The spectrum of Delta in the regular representation of H is the interval
[-1,1]. Let E(A), where A is a subset of [-1,1], be a family of spectral
projectors for Delta and m(A)=(E(A)e, e) be the corresponding spectral measure.
Here e is the characteristic function of the unit element of the group H. We
estimate the value m([-1,-1+t] \cup [1-t,1]) when t tends to 0. More precisely
we prove the inequality m([-1,-1+t] \cup [1-t,1]) > const t^{2+alpha} for any
positive alpha.
