Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: Haseo Ki
Journal: Proc. Amer. Math. Soc. 124 (1996), 3507-3514
MSC (1991): Primary 04A15, 26A21; Secondary 42A20
MathSciNet review: 1340391
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 04A15, 26A21, 42A20

Retrieve articles in all journals with MSC (1991): 04A15, 26A21, 42A20


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: http://dx.doi.org/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
Article copyright: © Copyright 1996 American Mathematical Society