Abstract
The approximate symmetric Henstock-Kurzweil integral is shown as solving the problem of the recovery of a function from its trigonometric integral. This being so, we generalize Offord's theorem, which is an analogue of de la Vallée Poussin's theorem for trigonometric series. A new condition for a function to be representable by a singular Fourier integral is also obtained. Bibliography: 10 titles.
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