Single Generator Problem

Junichi Tanaka*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Using the Stone-Čech compactification βZ of integers, we introduce a free extension of an almost periodic flow. Together with some properties of outer functions, we see that, in a certain class of ergodic Hardy spaces Hp(μ), 1 ≤ p ≤ ∞, the corresponding subspaces Ho p(μ) are all singly generated. This shows the existence of maximal weak-* Dirichlet algebras, different from H of the disc, for which the single generator problem is settled.

Original languageEnglish
Pages (from-to)4113-4129
Number of pages17
JournalTransactions of the American Mathematical Society
Issue number10
Publication statusPublished - 1996
Externally publishedYes


  • Cocycles
  • Ergodic hardy spaces
  • Outer functions
  • Single generators

ASJC Scopus subject areas

  • General Mathematics


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