In 1984, the second author proved that, after correction on a set of arbitrarily small measure, any continuous function on a finite-dimensional compact Abelian group acquires sparse spectrum and uniformly convergent Fourier series. In the present paper, we refine the result in two directions: first, we ensure uniform convergence in a stronger sense; second, we prove that the spectrum after correction can be put in even more peculiar sparse sets. Bibliography: 6 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 376, 2010, pp. 25–47.
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Ivanishvili, P., Kislyakov, S.V. Correction up to a function with sparse spectrum and uniformly convergent Fourier series. J Math Sci 172, 195–206 (2011). https://doi.org/10.1007/s10958-010-0192-7
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DOI: https://doi.org/10.1007/s10958-010-0192-7