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

Haseo Ki

Research output: Contribution to journal › Article

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 Fσδ. Also we prove that any Gδσ set that includes UCF must contain a continuous function with divergent Fourier series.

Original languageEnglish
Pages (from-to)3507-3514
Number of pages8
JournalProceedings of the American Mathematical Society
Volume124
Issue number11
Publication statusPublished - 1996 Dec 1

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Fourier series
Continuous Function
Divergent Series
Unit circle
Calculate
Hierarchy

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

Ki, Haseo. / On the set of all continuous functions with uniformly convergent Fourier series. In: Proceedings of the American Mathematical Society. 1996 ; Vol. 124, No. 11. pp. 3507-3514.
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Ki, H 1996, 'On the set of all continuous functions with uniformly convergent Fourier series', 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.

In: Proceedings of the American Mathematical Society, Vol. 124, No. 11, 01.12.1996, p. 3507-3514.

Research output: Contribution to journal › Article

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Ki H. On the set of all continuous functions with uniformly convergent Fourier series. Proceedings of the American Mathematical Society. 1996 Dec 1;124(11):3507-3514.

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