2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/140637We analyze representations of solvable Baumslag Solitar group that admit wavelets and show how such representations can be constructed from a given low-pass filter. We describe the direct integral decomposition for some examples and derive from it a general criterion for the existence of solutions for scaling equations. As another application, we construct a Fourier transform for some Hausdorff measures.Classical Analysis and ODEsOperator Algebras42C40, 28A78, 46L45, 28D05, 22D25text