The periodic dilation completeness problem: cyclic vectors in the Hardy space over the infinite‐dimensional polydisk

  title={The periodic dilation completeness problem: cyclic vectors in the Hardy space over the infinite‐dimensional polydisk},
  author={Hui Dan and Kunyu Guo},
  journal={Journal of the London Mathematical Society},
  • Hui Dan, K. Guo
  • Published 8 August 2019
  • Mathematics
  • Journal of the London Mathematical Society
The classical completeness problem raised by Beurling and independently by Wintner asks for which ψ∈L2(0,1) , the dilation system {ψ(kx):k=1,2,…} is complete in L2(0,1) , where ψ is identified with its extension to an odd 2‐periodic function on R . This difficult problem is nowadays commonly called as the periodic dilation completeness problem (PDCP). By Beurling's idea and an application of the Bohr transform, the PDCP is translated as an equivalent problem of characterizing cyclic vectors in… 
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