Single Generator Problem

Junichi Tanaka

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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
Volume348
Issue number10
Publication statusPublished - 1996
Externally publishedYes

Fingerprint

Almost Periodic
Hardy Space
Compactification
Algebra
Dirichlet
Subspace
Generator
Integer
Class

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Single Generator Problem. / Tanaka, Junichi.

In: Transactions of the American Mathematical Society, Vol. 348, No. 10, 1996, p. 4113-4129.

Research output: Contribution to journalArticle

Tanaka, J 1996, 'Single Generator Problem', Transactions of the American Mathematical Society, vol. 348, no. 10, pp. 4113-4129.
Tanaka, Junichi. / Single Generator Problem. In: Transactions of the American Mathematical Society. 1996 ; Vol. 348, No. 10. pp. 4113-4129.
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