2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107649This paper is an extended version of math.OA/0601528 where we point out and remedy a gap in the proof by P. Julg and G. Kasparov of the Baum-Connes conjecture for discrete subgroups of SU(n,1). In particular, here we explain in details why the non-microlocality of the Heisenberg calculus prevents us from implementing into this framework the classical approach of Seeley to pseudodifferential complex powers, which was the main issue at stake in math.OA/0601528.8 pages. Superceded by 2nd version of math.OA/0601528Analysis of PDEstext