Integrability of the Fourier transform: functions of bounded variation
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boundedfouriertransformvariationfunctionscertaincosinederivative
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Certain relations between the Fourier transform of a function of bounded variation and the Hilbert transform of its derivative are revealed. The widest subspaces of the space of functions of bounded variation are indicated in which the cosine and sine Fourier transforms are integrable.
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