Wednesday, September 12th, 2012
1:00pm - 2:00pm, in Science 2-064

Elijah Liflyand

Bar-Ilan University

Relations between the Fourier transform and the Hilbert transform

Abstract: n this talk we discuss various conditions of the integrability of the Fourier transform of a function of bounded variation and their connections to the behavior of the Hilbert transform of a related function. Correspondingly, the considered spaces of functions with integrable Fourier transform are intimately related with the real Hardy space. One of the most important connections for the two transforms is given by the space introduced (for different purposes) by Johnson and Warner.