|2018 Fall Physics Colloquium Series|
Tao Mei, Ph.D.
Department of Mathematics
An Introduction to Hilbert Transforms
For more information contact: Dr. Anzhong Wang 254-710-2276
Hilbert transform is a fundamental object in mathematics. It has various equivalent formulations. Let us consider the square integrable functions on the time interval [0,2π]. In this case, Hilbert transform is a linear map sending Cosine functions Cos(kt) to Sine functions Sin(kt) and sending Sine functions to the negative Cosines. This talk will be an introductory talk on the history and the ongoing mathematical research on the Hilbert transforms. The focus will be the boundedness of the Hilbert transform with respect to the Lp norms.