2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170870We study $p$-adic multiresolution analyses (MRAs). A complete characterisation of test functions generating a MRA (scaling functions) is given. We prove that only 1-periodic test functions may be taken as orthogonal scaling functions and that all such scaling functions generate Haar MRA. We also suggest a method of constructing sets of wavelet functions and prove that any set of wavelet functions generates a $p$-adic wavelet frame.17 pagesFunctional AnalysisNumber Theorytext