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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > The Fourier transform of a function of bounded variation: symmetry and asymmetry

## The Fourier transform of a function of bounded variation: symmetry and asymmetryAdd to your list(s) Download to your calendar using vCal - Elijah Liflyand (Bar-Ilan University)
- Thursday 24 January 2019, 15:00-16:00
- Seminar Room 2, Newton Institute.
If you have a question about this talk, please contact INI IT. ASC - Approximation, sampling and compression in data science New relations between the Fourier transform of a function of bounded variation and the Hilbert transform of its derivative are revealed. The main result is an asymptotic formula for the cosine Fourier transform. Such relations have previously been known only for the sine Fourier transform. To prove the mentioned result, not only a different space is considered but also a new way of proving such theorems is applied. Interrelations of various function spaces are studied in this context. The obtained results are used for proving new estimates for the Fourier transform of a radial function and completely new results on the integrability of trigonometric series. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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