Abstract
Certain relations between the Fourier transform of a function and the Hilbert transform of its derivative are revealed. They concern the integrability/non-integrability of both transforms. Certain applications are discussed.
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Dedicated to the 75-th birthday of R. M. Trigub
Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 9, No. 2, pp. 209–218, April–May, 2012.
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Liflyand, E. Fourier transform versus Hilbert transform. J Math Sci 187, 49–56 (2012). https://doi.org/10.1007/s10958-012-1048-0
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DOI: https://doi.org/10.1007/s10958-012-1048-0