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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the set of all continuous functions with uniformly convergent Fourier series
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by Haseo Ki PDF
Proc. Amer. Math. Soc. 124 (1996), 3507-3514 Request permission

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 $F_{\sigma \delta }.$ Also we prove that any $G_{\delta \sigma }$ set that includes $UCF$ must contain a continuous function with divergent Fourier series.
References
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Additional Information
  • Haseo Ki
  • Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
  • Address at time of publication: GARC, Department of Mathematics, Seoul National University, Seoul 151-742, Korea
  • Received by editor(s): May 26, 1994
  • Received by editor(s) in revised form: May 12, 1995
  • Additional Notes: The author was partially supported by GARC-KOSEF
  • Communicated by: Andreas R. Blass
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 3507-3514
  • MSC (1991): Primary 04A15, 26A21; Secondary 42A20
  • DOI: https://doi.org/10.1090/S0002-9939-96-03447-8
  • MathSciNet review: 1340391