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Democratic systems of translates. (English) Zbl 1290.41023

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 \(\psi\).

MSC:

41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
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