Exploring the power of nonlinearity in complex function theory (in 1 d and higher dimensions)

Event time: 
Thursday, January 26, 2023 - 4:15pm
Ronald Coifman
Speaker affiliation: 
Yale University
Event description: 

We describe recent remarkable nonlinear analytic approximation tools in the classical setting of Hardy spaces in the upper half plane and show how to transfer them to the higher dimensional real setting of harmonic functions in upper half spaces. It is known that all harmonic functions in higher dimensions are combinations of holomorphic functions on 2 dimensional planes, extended as, constant in normal directions. We derive representation theorems, with corresponding isometries, opening the door for applications in higher dimensions, to the processing of highly oscillatory multidimensional signals.

This is joint work with Guido Weiss Stefan Steinerberger , Jacques Peyriere , Hau -tieng Wu and many othersĀ