  Let $P$ be a generalized laplacian on $R^{2n+1}$. It is known that $P$ is the
generating functional of semigroups of measures $\mu_{t}$ on the Heisenberg
group $H^{n}$ and $\nu_{t}$ on the Abelian group $R^{2n+1}$. Under some
smoothness and growth conditions on the functional $P$ expressed in terms of
its Abelian Fourier transform $\widehat{P}$ we show that the semigroup
$\mu_{t}$ is a kind of perturbation of the semigroup $\nu_{t}$. More precisely,
we give pointwise estimates for the difference of the densities of the measures
$\mu_{t}$ and $\nu_{t}$.
  As a consequence we get a description of the asymptotic behavior at the
origin or pointwise estimates for the densities of the semigroup of measures on
the Heisenberg group which is an analogue (via generating functional) of the
symmetrized gamma (gamma-variance) semigroup on $R^{2n+1}$.
  The main tool is a symbolic calculus for convolution operators on the
Heisenberg group.
