  In this work we define operator-valued Fourier transforms for suitable
integrable elements with respect to the Plancherel weight of a (not necessarily
Abelian) locally compact group. Our main result is a generalized version of the
Fourier inversion Theorem for strictly-unconditionally integrable Fourier
transforms. Our results generalize and improve those previously obtained by Ruy
Exel in the case of Abelian groups.
