2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/132577Motivated by the multivariate wavelet theory, and by the spectral theory of transfer operators, we construct an abstract affine structure and a multiresolution associated to a matrix-valued weight. We describe the one-to-one correspondence between the commutant of this structure and the fixed points of the transfer operator. We show how the covariant representation can be realized on $\mathbb{R}^n$ if the weight satisfies some low-pass condition.new version, motivation addedFunctional AnalysisDynamical Systems37C40, 37A55, 42C40text