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Topics in Time-Frequency analysis
PDE & Applied Mathematics| Speaker: | Victor Lie, Purdue |
| Location: | 2112 MSB |
| Start time: | Thu, Feb 19 2015, 4:10PM |
Description
This is intended to be a talk for a (more) general audience. The
plan of it is as follows: we start by discussing several facts about the history
and evolution of the time-frequency area (Fourier Series, Calderon-Zygmund
theory, wave-packet theory) and then refer to the general approach/tools
for solving a time-frequency problem. Next we present two fundamental
topics in this eld: the pointwise convergence of the Fourier Series and the
boundedness of the Bilinear Hilbert transform. We end by adressing several
key aspects of our work including the following problems:
-- the boundedness of the Bilinear Hilbert transform on smooth curves;
-- the boundedness of the Polynomial Carleson operator;
-- the pointwise convergence of Fourier Series near L1.