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 -