Colombeau's generalized functions on a manifold.
The commutative neutrix convolution product of the functions and is evaluated for and all . Further commutative neutrix convolution products are then deduced.
Let L(z) be the Lie norm on and L*(z) the dual Lie norm. We denote by the space of complex harmonic functions on the open Lie ball and by the space of entire harmonic functions of exponential type (A,L*). A continuous linear functional on these spaces will be called a harmonic functional or an entire harmonic functional. We shall study the conical Fourier-Borel transformations on the spaces of harmonic functionals or entire harmonic functionals.