The Set of Continuous Functions with the Everywhere Convergent Fourier Series

Keywords

Mathematics, Almost everywhere, Fourier series, Countable set, Differentiable function

References

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• Treatise of Trigonometric SeriesA. Zygmund, N.K. BARY — 1966
• The set of continuous nowhere differentiable functionsR. Daniel Mauldin — 1979
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• Sets of divergence of Taylor series and of trigonometric seriesP. Erdös, Fritz Herzog, George Piranian — 1954
• Introduction to classical real analysisLucy Clarke — 1981
• Trigonometric SeriesPhilip Heywood — 1968
• Functional analysisWalter Rudin — 1973
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• An Introduction to Harmonic Analysis.Guido Weiss, Yitzhak Katznelson — 1970

Cited by

• On the Denjoy rank, the Kechris-Woodin rank and the Zalcwasser rankHaseo Ki — 1997
• On the set of all continuous functions with uniformly convergent Fourier seriesHaseo Ki — 1996
• Topics In Descriptive Set Theory Related To Number Theory and AnalysisHaseo Ki — 1995
• Fractal and infinitely differentiable functions in compactly supported control problems for hyperbolic distributed systemsА. Н. Агаджанов — 2008
• The Kechris-Woodin rank is finer than the Zalcwasser rankHaseo Ki — 1995
• Three ordinal ranks for the set of differentiable functionsT. I. Ramsamujh — 1991
• Simply Connected Compact Subsets of the PlaneT. I. Ramsamujh — 1999
• Uniqueness of trigonometric series and descriptive set theory, 1870–1985Roger Cooke — 1993
• Ranks of differentiable functionsAlexander S. Kechris, W. Hugh Woodin — 1986
• Some examples of Borel-inseparable pairs of coanalylic setsHoward Becker — 1986
• The Complexity of Everywhere Divergent Fourier SeriesT. I. Ramsamujh — 1991
• The Complexity Of Nowhere Differentiable Continuous FunctionsT. I. Ramsamujh — 1989
• Computable structures and operations on the space of continuous functionsAlexander Melnikov, Keng Meng Ng — 2016
• A Generalization of Pisier Homogeneous Banach AlgebraSafari Mukeru — 2021
• Set descriptive complexity of solvable functionsGozzi Riccardo, Olivier Bournez — 2024
• Descriptive Set Theoretic Phenomena in Analysis and TopologyBecker — 1990

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