Heaviside Operators on Quantum Phase Space

By means of Heaviside operational schemes, formal differential operators [i.e., Arbitrary functions of the derivative symbols] are realised as convolution operators on the prescribed class of operands. This connection allows an alternative framework for momentum and configuration space dependence of quantum operators acting on phase space generalisation of the wavefunction in a phase space representation of quantum dynamics. Applying the formal Heaviside ansatz to the resulting wave equations reduces them to exact quadratures