Integrability of the Fourier transform: functions of bounded variation
Classical Analysis and ODEs
2012-01-27 v1
Abstract
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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Cite
@article{arxiv.1201.5558,
title = {Integrability of the Fourier transform: functions of bounded variation},
author = {E. Liflyand},
journal= {arXiv preprint arXiv:1201.5558},
year = {2012}
}
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7 pages