### Abstract

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 language | English |
---|---|

Pages (from-to) | 87-90 |

Number of pages | 4 |

Journal | Proceedings of the American Mathematical Society |

Volume | 69 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1978 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*69*(1), 87-90. https://doi.org/10.1090/S0002-9939-1978-0482594-1

**A note on helson's existence theorem.** / Tanaka, Junichi.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 69, no. 1, pp. 87-90. https://doi.org/10.1090/S0002-9939-1978-0482594-1

}

TY - JOUR

T1 - A note on helson's existence theorem

AU - Tanaka, Junichi

PY - 1978

Y1 - 1978

N2 - 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.

AB - 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.

KW - Distant future

KW - Ergodic measure

KW - Invariant subspace

KW - Outer function

KW - Weak- dirichlet algebra

UR - http://www.scopus.com/inward/record.url?scp=84968488980&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84968488980&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1978-0482594-1

DO - 10.1090/S0002-9939-1978-0482594-1

M3 - Article

VL - 69

SP - 87

EP - 90

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 1

ER -