  We study non-abelian versions of the Mellin transformations, originally
introduced by Gabber-Loeser on complex affine tori. Our main result is a
generalization to the non-abelian context and with arbitrary coefficients of
the t-exactness of Gabber-Loeser's Mellin transformation. As an intermediate
step, we obtain vanishing results for the Sabbah specialization functors. Our
main application is to construct new examples of duality spaces in the sense of
Bieri-Eckmann, generalizing results of Denham-Suciu.
