Democratic systems of translates (Q390502)

Democratic systems arise in the context of greedy approximations in Banach spaces. Systems of translates of a single function are used in the construction of wavelets and a Gabor system. There is a natural question to be answered. Consider a system of integer translations of a single function \(\psi\in L^2(\mathbb R)\). What are necessary and sufficient conditions for such a system to be democratic? In general, this problem is still unsolved. In the paper under review, the authors give several necessary and sufficient criteria in terms of properties of \(\psi\).