非线性傅立叶变换的点收敛性 | 数学年鉴

IF 5.7 1区数学 Q1 MATHEMATICS

Annals of Mathematics Pub Date : 2024-03-05 DOI:10.4007/annals.2024.199.2.4

A. Poltoratski

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引用次数: 0

摘要

我们证明了狄拉克微分方程系统散射数据的点收敛性。等效地，我们证明了 Carleson 关于非线性傅里叶变换版本的傅里叶级数几乎无处不收敛的类似定理。我们的证明基于对狄拉克系统共振的研究，使用的是由与该系统相对应的里卡蒂方程所产生的并行内函数族。

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Pointwise convergence of the non-linear Fourier transform | Annals of Mathematics

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.

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来源期刊

Annals of Mathematics 数学-数学

CiteScore

9.10

自引率

2.00%

发文量

审稿时长

12 months

期刊介绍： The Annals of Mathematics is published bimonthly by the Department of Mathematics at Princeton University with the cooperation of the Institute for Advanced Study. Founded in 1884 by Ormond Stone of the University of Virginia, the journal was transferred in 1899 to Harvard University, and in 1911 to Princeton University. Since 1933, the Annals has been edited jointly by Princeton University and the Institute for Advanced Study.