Session S30 - Mathematical Methods in Quantum Mechanics

Friday, July 16, 16:00 ~ 16:40 UTC-3

Pointwise convergence for the non-linear Fourier transform

Alexei Poltoratski

University of Wisconsin - Madison, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

It is widely understood that the scattering transform can be viewed as an analog of the Fourier transform in non-linear settings. This connection brings up numerous questions on finding non-linear analogs of classical results of Fourier analysis. One of the fundamental results of harmonic analysis is the theorem by L. Carleson on pointwise convergence of the Fourier series. In this talk I will discuss convergence for the scattering data of a real Dirac system on the half-line and present an analog of Carleson's theorem for the non-linear Fourier transform.

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