Abstract
We show that any bounded nonnegative lower semicontinuous function is the modulus of some function with uniformly bounded Fourier series partial sums. A simple proof is given of the (familiar) theorem that any measurable function can be altered on a set of arbitrarily small measure so as to become a function whose Fourier and Fourier-Walsh series converge.
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Literature cited
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 135, pp. 69–75, 1984.
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Kislyakov, S.V. Remarks on “correcting”. J Math Sci 31, 2682–2686 (1985). https://doi.org/10.1007/BF02107251
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DOI: https://doi.org/10.1007/BF02107251