2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224506In 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.15 pages; some typos correctedFunctional AnalysisOperator Algebras43A30; 43A35; 43A50text