Parabolic wavelet transforms associated with the singular heat operators -D
elta gamma + partial derivative/partial derivativet and I-Delta gamma + par
tial derivative/partial derivativet, where Delta gamma = Sigma (n)(k=l) par
tial derivative (2)/partial derivativex(k)(2) + (2 gamma /x(n))partial deri
vative/partial derivativex(n), are introduced. These transforms are defined
in terms of the relevant generalized translation operator. An analogue of
the Calderon reproducing formula is established. New inversion formulas are
obtained for generalized parabolic potentials representing negative powers
of the singular heat operators.