Pointwise convergence of scattering data

5 Jul 2021, 15:55


Alexei Poltoratski (University of Wisconsin-Madison)


The scattering transform, appearing in the study of differential operators, 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 linear analysis is a 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.

Primary author

Alexei Poltoratski (University of Wisconsin-Madison)

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