On the set of all continuous functions with uniformly convergent Fourier series
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- by Haseo Ki
- Proc. Amer. Math. Soc. 124 (1996), 3507-3514
- DOI: https://doi.org/10.1090/S0002-9939-96-03447-8
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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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Bibliographic 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