Geodesic
Correction up to a function with sparse spectrum and uniformly convergent Fourier series
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 38, Tome 376 (2010), pp. 25-47 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. Bibl. – 6 titles. 
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P. Ivanishvili; S. V. Kislyakov. Correction up to a function with sparse spectrum and uniformly convergent Fourier series. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 38, Tome 376 (2010), pp. 25-47. http://geodesic.mathdoc.fr/item/ZNSL_2010_376_a1/

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