Parabolic potentials and wavelet transforms with the generalized translation (Q2717561)

The authors consider the singular heat operators \(-\Delta_\gamma+ {\partial\over\partial t}\) and \(I- \Delta_\gamma+{\partial\over\partial t}\) where \(\Delta_\gamma= \sum^n_{k=1} {\partial^2\over\partial x^2_k}+ {2\gamma\over x_n} {\partial\over\partial x_n}\), \(\gamma> 0\). He introduces the parabolic wavelet transforms associated with these operators, and he establishes an analogue of the Calderón reproducing formula. Next, he gives inversion formulas for generalized parabolic potentials representing negative powers of the singular heat operators.