Abstract
We prove pointwise convergence for the scattering data of a Dirac system of differential equations. Equivalently, we prove an analog of Carleson's theorem on almost everywhere convergence of Fourier series for a version of the non-linear Fourier transform. Our proofs are based on the study of resonances of Dirac systems using families of meromorphic inner functions, generated by a Riccati equation corresponding to the system.
Citation
A. Poltoratski. "Pointwise convergence of the non-linear Fourier transform." Ann. of Math. (2) 199 (2) 741 - 793, March 2024. https://doi.org/10.4007/annals.2024.199.2.4
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