  In this article wavelets (admissible vectors) on the Heisenberg group are
studied from the point of view of Calderon's formula. Further we shall show
that for the class of Schwartz functions the Calderon admissibility condition
is equivalent to the usual admissibility property which will be introduced in
this work. Furthermore motivated by a well-known example on the real line, the
Mexican-Hat wavelet, we demonstrate the existence and construction of an
analogous wavelet on the Heisenberg Lie group with 2 vanishing moments, which
together with all of its derivatives has Gaussian decay.
