Riesz multiresolution analysis on Vilenkin groups (Q483646)

The Vilenkin group \(G_p\) can be defined as the weak direct product of a countable number of the cyclic groups of order \(p\). For this group, the family of compactly supported orthogonal MRA-based wavelets are provided in [\textit{Y. A. Farkov} and \textit{E. A. Rodionov}, \(p\)-Adic Numbers Ultrametric Anal. Appl. 3, No. 3, 181--195 (2011; Zbl 1254.42044)]. The author proposes a method for constructing an MRA with a Riesz basis in \(L^2(G_p)\). In more detail this method is presented in [the author, ``Riesz multiresolution analysis on zero-dimensional groups'', Izv. Ross. Akad. Nauk Ser. Mat. 79, No. 1, 153--184 (2015; \url{doi:10.1070/IM2015v079n01ABEH002737})].