Title: Hilbert transforms, old and new stories
Speaker: Tao Mei, Baylor University
Abstract: This talk will be on the Lp boundedness of the Hilbert transform. This transform is the linear map on 2-integrable functions, which keep the analytic part of the functions and reverse the sign of their anti-analytic part. In the language of Fourier analysis, the Hilbert transform is a Fourier multiplier with symbol ``-isign (x)”.
This talk will introduce some new discovery of Hilbert transforms on free groups, based on a joint work with Eric Ricard. I plan to start with the history of trigonometric functions. If time permits, I will also explain a recent work with Quanhua Xu in this direction.
Time: 13 July, 9:30-10:30, Place: 522 Gewu Building
