### 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Transactions of the American Mathematical Society*,

*348*(10), 4113-4129.

**Single Generator Problem.** / Tanaka, Junichi.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 348, no. 10, pp. 4113-4129.

}

TY - JOUR

T1 - Single Generator Problem

AU - Tanaka, Junichi

PY - 1996

Y1 - 1996

N2 - 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.

AB - 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.

KW - Cocycles

KW - Ergodic hardy spaces

KW - Outer functions

KW - Single generators

UR - http://www.scopus.com/inward/record.url?scp=33645944061&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645944061&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33645944061

VL - 348

SP - 4113

EP - 4129

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 10

ER -