p-ADIC MULTIRESOLUTION ANALYSES

S. ALBEVERIO, S. EVDOKIMOV, AND M. SKOPINAAbstract. We study p-adic multiresolution analyses (MRAs). A completecharacterisation of test functions generating a MRA (scaling functions) isgiven. We prove that only 1-periodic test functions may be taken as orthogo-nal scaling functions and that all such scaling functions generate Haar MRA.We also suggest a method of constructing sets of wavelet functions and provethat any set of wavelet functions generates a p-adic wavelet frame.