### 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 H^{p}(μ), 1 ≤ p ≤ ∞, the corresponding subspaces H_{o}
^{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 language | English |
---|---|

Pages (from-to) | 4113-4129 |

Number of pages | 17 |

Journal | Transactions of the American Mathematical Society |

Volume | 348 |

Issue number | 10 |

Publication status | Published - 1996 |

Externally published | Yes |

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Single Generator Problem'. Together they form a unique fingerprint.

## Cite this

Tanaka, J. (1996). Single Generator Problem.

*Transactions of the American Mathematical Society*,*348*(10), 4113-4129.