  In this work, a general definition of convolution between two arbitrary
Ultradistributions of Exponential type (UET) is given. The product of two
arbitrary UET is defined via the convolution of its corresponding Fourier
Transforms. Some examples of convolution of two UET are given. Expressions for
the Fourier Transform of spherically symmetric (in Euclidean space) and Lorentz
invariant (in Minkowskian space) UET in term of modified Bessel distributions
are obtained (Generalization of Bochner's theorem). The generalization to UET
of dimensional regularization in configuration space is obtained in both,
Euclidean and Minkowskian spaces As an application of our formalism, we give a
solution to the question of normalization of resonances in Quantum Mechanics.
General formulae for convolution of even, spherically symmetric and Lorentz
invariant UET are obtained and several examples of application are given.
