Wavelet tight frames in Walsh analysis

Abstract. We describe two type of wavelet tight frames associated with the generalized Walsh functions: (1) Parseval frames for \(L^2\)-spaces on Vilenkin groups, (2) finite tight frames for the space \(\ell^2({\mathbb Z}_N)\). In particular cases these tight frames coincide with orthogonal wavelet bases associated with the classical Walsh functions.

Key words and phrases. Walsh functions, wavelets, tight frames, Parseval frames, Cantor group, Vilenkin groups.