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The Fourier transform of a function of bounded variation: symmetry and asymmetry

Presented by: 
Elijah Liflyand Bar-Ilan University
Thursday 24th January 2019 - 15:00 to 16:00
INI Seminar Room 2
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.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons