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

Haseo Ki

doi:10.1090/s0002-9939-96-03447-8

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

Haseo Ki

Department of Mathematics

Research output: Contribution to journal › Article

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_σδ. Also we prove that any G_δσ set that includes UCF must contain a continuous function with divergent Fourier series.

Original language	English
Pages (from-to)	3507-3514
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	124
Issue number	11
DOIs	https://doi.org/10.1090/s0002-9939-96-03447-8
Publication status	Published - 1996

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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Ki, H. (1996). On the set of all continuous functions with uniformly convergent Fourier series. Proceedings of the American Mathematical Society, 124(11), 3507-3514. https://doi.org/10.1090/s0002-9939-96-03447-8

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