{"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}
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.
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.
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