2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/154425We study $p$-adic multiresolution analyses (MRAs). A complete characterisation of test functions generating MRAs (scaling functions) is given. We prove that only 1-periodic test functions may be taken as orthogonal scaling functions. We also suggest a method for the construction of wavelet functions and prove that any wavelet function generates a $p$-adic wavelet frame.16 pagesClassical Analysis and ODEs42C40; 11F85text