A note on helson's existence theorem

Junichi Tanaka*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


In the almost periodic context, Helson showed that there exists a unitary function in every simply invariant subspace. We provide a short proof of this result in more general setting and give some applications.

Original languageEnglish
Pages (from-to)87-90
Number of pages4
JournalProceedings of the American Mathematical Society
Issue number1
Publication statusPublished - 1978
Externally publishedYes


  • Distant future
  • Ergodic measure
  • Invariant subspace
  • Outer function
  • Weak-* dirichlet algebra

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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