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On the set of all continuous functions with uniformly convergent Fourier series
Author(s):
Haseo
Ki
Journal:
Proc. Amer. Math. Soc.
124
(1996),
3507-3514.
MSC (1991):
Primary 04A15, 26A21;
Secondary 42A20
MathSciNet review:
1340391
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Abstract:
In this article we calculate the exact location in the Borel hierarchy of  the set of all continuous functions on the unit circle with uniformly convergent Fourier series. It turns out to be complete  Also we prove that any  set that includes  must contain a continuous function with divergent Fourier series.
References:
- [AK]
- M. Ajtai and A. S. Kechris, The set of continuous functions with everywhere convergent Fourier series, Trans. Amer. Math. Soc. 302 (1987), 207--221. MR 89b:04005
- [Ka]
- Y. Katznelson, An introduction to harmonic analysis, Dover, New York, 1976. MR 54:10976
- [Ke]
- Alexander S. Kechris, Classical Descriptive Set Theory, Springer Verlag, 1995. CMP 95:09
- [KL]
- Haseo Ki and Tom Linton, Normal numbers and subsets of
 with given densities, Fundamenta Mathematicae (2) 144 (1994), 163--179. MR 95e:04005 - [Zy]
- A. Zygmund, Trigonometric series, 2nd ed., Cambridge Univ. Press, 1959. MR 21:6498
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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
DOI:
10.1090/S0002-9939-96-03447-8
PII:
S 0002-9939(96)03447-8
Keywords:
Descriptive set theory,
Fourier series,
complete $F_{\sigma \delta }$,
uniformly convergent Fourier series
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 of article:
Copyright
1996,
American Mathematical Society
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