2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167019We analyze matrix-valued transfer operators. We prove that the fixed points of transfer operators form a finite dimensional $C^*$-algebra. For matrix weights satisfying a low-pass condition we identify the minimal projections in this algebra as correlations of scaling functions, i.e., limits of cascade algortihms.v2, corrected some typosFunctional AnalysisDynamical Systems37C40, 37A55, 42C40text