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Sets of uniqueness for a certain class $ \mathcal{M}_\varepsilon$ on the dyadic group


Author: Kaoru Yoneda
Journal: Proc. Amer. Math. Soc. 89 (1983), 279-284
MSC: Primary 42C25; Secondary 42C10, 43A70
DOI: https://doi.org/10.1090/S0002-9939-1983-0712637-0
MathSciNet review: 712637
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Abstract: For each sequence $ \varepsilon = \left\{ {{\varepsilon _n}} \right\}$ of real numbers which satisfies $ \lim {\inf _{n \to \infty }}{\varepsilon _{{2^{n + 1}}}}/{\varepsilon _{{2^n}}} > 0$ and $ {\varepsilon _n} \downarrow 0$ as $ n \to \infty $, let $ {\mathfrak{M}_\varepsilon }$ denote the set of all Walsh series $ \mu \sim \sum\nolimits_{k = 0}^\infty {\hat \mu (k){w_k}(x)} $ such that $ \sum\nolimits_{k = 0}^\infty {{\varepsilon _k}{{\left\vert {\hat \mu (k)} \right\vert}^2} < \infty } $. We give a necessary and sufficient condition for a subset of the dyadic group to be a set of uniqueness for $ {\mathfrak{M}_\varepsilon }$.


References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/S0002-9939-1983-0712637-0
Article copyright: © Copyright 1983 American Mathematical Society

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