Pointwise convergence of the non-linear Fourier transform

• 成果类型: Article
• 署名作者: Poltoratski, A.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2024.199.2.4
• 发表日期: 2024
• 页码: 741-793
• 关键词: universality limits

摘要

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.