Finite Adelic Wavelet Bases and a Pseudodifferential Equation

In this article we apply a polyadic approach to obtain very explicit description of a novel kind of wavelets on the ring of finite adèles, \(\mathbb{A}_{f}\) , which are also eigenfunctions of a Vladimirov-type pseudodifferential operator on \(L^2(\mathbb{A}_{f})\) . As an accompaniment, we solve the Cauchy problem for a certain pseudodifferential equation.