2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68394In a series of papers, we have shown that from the representation theory of a compact groupoid one can reconstruct the groupoid using the procedure similar to the Tannaka-Krein duality for compact groups. In this part we study the Fourier and Fourier-Plancherel transforms and prove the Plancherel theorem for compact groupoids. We also study the central functions in the algebra of square integrable functions on the isotropy groups.14 pagesOperator Algebras43A30, 43A65text