On the translates of general dyadic systems on $${{\mathbb {R}}}$$
On the translates of general dyadic systems on $${{\mathbb {R}}}$$
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关于 $${{mathbb {R}}}$$ 上一般二元系统的翻译
DOI：
10.1007/s00208-019-01951-z
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发表时间：
2020
影响因子：
1.4
通讯作者：
Wei, Zeyu
中科院分区：
文献类型：
--
作者：
Anderson, Theresa C.;Hu, Bingyang;Jiang, Liwei;Olson, Connor;Wei, Zeyu
Many techniques in harmonic analysis use the fact that a continuous object can be written as a sum (or an intersection) of dyadic counterparts, as long as those counterparts belong to an adjacent dyadic system. Here we generalize the notion of adjacent dyadic system and explore when it occurs, leading to some new and perhaps surprising classifications. In particular, we show that every dyadic grid is determined by two parameters, theshiftand thelocation; moreover two dyadic grids form an adjacent dyadic system if and only if their shifts and locations satisfy readily verifiable conditions.
