{"title":"Decoupling inequalities for short generalized Dirichlet sequences","authors":"Yuqiu Fu, Larry Guth, Dominique Maldague","doi":"10.2140/apde.2023.16.2401","DOIUrl":null,"url":null,"abstract":"<p>We study decoupling theory for functions on <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>ℝ</mi></math> with Fourier transform supported in a neighborhood of short Dirichlet sequences <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msubsup><mrow><mo stretchy=\"false\">{</mo><mi>log</mi><mo> <!--FUNCTION APPLICATION--> </mo><!--nolimits--><mi>n</mi><mo stretchy=\"false\">}</mo></mrow><mrow><mi>n</mi><mo>=</mo><mi>N</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>N</mi><mo>+</mo><msup><mrow><mi>N</mi></mrow><mrow><mn>1</mn><mo>∕</mo><mn>2</mn></mrow></msup>\n</mrow></msubsup></math>, as well as sequences with similar convexity properties. We utilize the wave packet structure of functions with frequency support near an arithmetic progression. </p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2140/apde.2023.16.2401","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
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Abstract
We study decoupling theory for functions on with Fourier transform supported in a neighborhood of short Dirichlet sequences , as well as sequences with similar convexity properties. We utilize the wave packet structure of functions with frequency support near an arithmetic progression.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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