### Abstract

In this article we calculate the exact location in the Borel hierarchy of UCF, the set of all continuous functions on the unit circle with uniformly convergent Fourier series. It turns out to be complete F_{σδ}. Also we prove that any G_{δσ} set that includes UCF must contain a continuous function with divergent Fourier series.

Original language | English |
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Pages (from-to) | 3507-3514 |

Number of pages | 8 |

Journal | Proceedings of the American Mathematical Society |

Volume | 124 |

Issue number | 11 |

Publication status | Published - 1996 Dec 1 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

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*Proceedings of the American Mathematical Society*, vol. 124, no. 11, pp. 3507-3514.

**On the set of all continuous functions with uniformly convergent Fourier series.** / Ki, Haseo.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the set of all continuous functions with uniformly convergent Fourier series

AU - Ki, Haseo

PY - 1996/12/1

Y1 - 1996/12/1

N2 - In this article we calculate the exact location in the Borel hierarchy of UCF, the set of all continuous functions on the unit circle with uniformly convergent Fourier series. It turns out to be complete Fσδ. Also we prove that any Gδσ set that includes UCF must contain a continuous function with divergent Fourier series.

AB - In this article we calculate the exact location in the Borel hierarchy of UCF, the set of all continuous functions on the unit circle with uniformly convergent Fourier series. It turns out to be complete Fσδ. Also we prove that any Gδσ set that includes UCF must contain a continuous function with divergent Fourier series.

UR - http://www.scopus.com/inward/record.url?scp=33645920315&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645920315&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33645920315

VL - 124

SP - 3507

EP - 3514

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 11

ER -