TY - JOUR
T1 - On the set of all continuous functions with uniformly convergent Fourier series
AU - Ki, Haseo
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 1996
Y1 - 1996
N2 - 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 Fσδ. Also we prove that any Gδσ set that includes UCF must contain a continuous function with divergent Fourier series.
AB - 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 Fσδ. Also we prove that any Gδσ set that includes UCF must contain a continuous function with divergent Fourier series.
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U2 - 10.1090/s0002-9939-96-03447-8
DO - 10.1090/s0002-9939-96-03447-8
M3 - Article
AN - SCOPUS:33645920315
VL - 124
SP - 3507
EP - 3514
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 11
ER -