非线性傅立叶变换的点收敛性 | 数学年鉴

IF 8.3 2区材料科学 Q1 MATERIALS SCIENCE, MULTIDISCIPLINARY

ACS Applied Materials & Interfaces Pub Date : 2024-03-05 DOI:10.4007/annals.2024.199.2.4

A. Poltoratski

{"title":"非线性傅立叶变换的点收敛性 | 数学年鉴","authors":"A. Poltoratski","doi":"10.4007/annals.2024.199.2.4","DOIUrl":null,"url":null,"abstract":"<p>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.</p>","PeriodicalId":5,"journal":{"name":"ACS Applied Materials & Interfaces","volume":null,"pages":null},"PeriodicalIF":8.3000,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Pointwise convergence of the non-linear Fourier transform | Annals of Mathematics\",\"authors\":\"A. Poltoratski\",\"doi\":\"10.4007/annals.2024.199.2.4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>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.</p>\",\"PeriodicalId\":5,\"journal\":{\"name\":\"ACS Applied Materials & Interfaces\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":8.3000,\"publicationDate\":\"2024-03-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Materials & Interfaces\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4007/annals.2024.199.2.4\",\"RegionNum\":2,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATERIALS SCIENCE, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Materials & Interfaces","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4007/annals.2024.199.2.4","RegionNum":2,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATERIALS SCIENCE, MULTIDISCIPLINARY","Score":null,"Total":0}

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

ACS Applied Materials & Interfaces 工程技术-材料科学：综合

CiteScore

16.00

自引率

6.30%

发文量

4978

审稿时长

1.8 months

期刊介绍： ACS Applied Materials & Interfaces is a leading interdisciplinary journal that brings together chemists, engineers, physicists, and biologists to explore the development and utilization of newly-discovered materials and interfacial processes for specific applications. Our journal has experienced remarkable growth since its establishment in 2009, both in terms of the number of articles published and the impact of the research showcased. We are proud to foster a truly global community, with the majority of published articles originating from outside the United States, reflecting the rapid growth of applied research worldwide.