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

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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
Issue number11
Publication statusPublished - 1996 Dec 1


All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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