@ARTICLE{Anderson2020-jv,
  title     = "On the translates of general dyadic systems on
               $${{\textbackslashmathbb {{R}}}$$}",
  author    = "Anderson, Theresa C and Hu, Bingyang and Jiang, Liwei and Olson,
               Connor and Wei, Zeyu",
  abstract  = "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,
               the shift and the location; moreover two dyadic grids form an
               adjacent dyadic system if and only if their shifts and locations
               satisfy readily verifiable conditions.",
  journal   = "Math. Ann.",
  publisher = "Springer Science and Business Media LLC",
  volume    =  377,
  number    = "3-4",
  pages     = "911--933",
  month     =  aug,
  year      =  2020,
  language  = "en"
}