2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119882We give an analytic proof of the fact that the index of an elliptic operator on the boundary of a compact manifold vanishes when the principal symbol comes from the restriction of a $K$-theory class from the interior. The proof uses noncommutative residues inside the calculus of cusp pseudodifferential operators of Melrose.10 pagesAnalysis of PDEsK-Theory and Homology58J20,58J42text