On the set of all continuous functions with uniformly convergent Fourier series
HTML articles powered by AMS MathViewer
- 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
- M. Ajtai and A. S. Kechris, The set of continuous functions with everywhere convergent Fourier series, Trans. Amer. Math. Soc. 302 (1987), no. 1, 207–221. MR 887506, DOI 10.1090/S0002-9947-1987-0887506-4
- Yitzhak Katznelson, An introduction to harmonic analysis, Second corrected edition, Dover Publications, Inc., New York, 1976. MR 0422992
- Alexander S. Kechris, Classical Descriptive Set Theory, Springer Verlag, 1995.
- Haseo Ki and Tom Linton, Normal numbers and subsets of $\mathbf N$ with given densities, Fund. Math. 144 (1994), no. 2, 163–179. MR 1273694
- A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776
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