Integrability of the Fourier transform: functions of bounded variation

Details Integrability of the Fourier transform: functions of bounded variation Integrability of the Fourier transform: functions of bounded variation

2012-01-26

arxiv.org/abs/1201.5558v1

Mathematics

Classical Analysis and ODEs

7 pages

Scientific paper

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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