齐次自仿射测度的傅立叶衰减

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-05-17 DOI:10.4171/jfg/119

B. Solomyak

{"title":"齐次自仿射测度的傅立叶衰减","authors":"B. Solomyak","doi":"10.4171/jfg/119","DOIUrl":null,"url":null,"abstract":"lim p μpξq “ 0, as |ξ| Ñ 8, where |ξ| is a norm (say, the Euclidean norm) of ξ P Rd. Whereas absolutely continuous measures are Rajchman by the Riemann-Lebesgue Lemma, it is a subtle question to decide which singular measures are such, see, e.g., the survey of Lyons [14]. A much stronger property, useful for many applications is the following. Definition 1.1. For α ą 0 let Ddpαq “ ν finite positive measure on Rd : |p νptq| “ Oνp|t|q, |t| Ñ 8 (","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2021-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Fourier decay for homogeneous self-affine measures\",\"authors\":\"B. Solomyak\",\"doi\":\"10.4171/jfg/119\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"lim p μpξq “ 0, as |ξ| Ñ 8, where |ξ| is a norm (say, the Euclidean norm) of ξ P Rd. Whereas absolutely continuous measures are Rajchman by the Riemann-Lebesgue Lemma, it is a subtle question to decide which singular measures are such, see, e.g., the survey of Lyons [14]. A much stronger property, useful for many applications is the following. Definition 1.1. For α ą 0 let Ddpαq “ ν finite positive measure on Rd : |p νptq| “ Oνp|t|q, |t| Ñ 8 (\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2021-05-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/jfg/119\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/jfg/119","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 6

摘要

lim pμpξq“0，如|ξ|ñ8，其中|ξ|r是ξp Rd的范数（比如欧几里得范数）。虽然绝对连续测度是Riemann-Lebesgue引理的Rajchman，但决定哪些奇异测度是这样的是一个微妙的问题，例如参见Lyons的调查[14]。一个更强的性质，对许多应用都有用，如下定义1.1。设Ddpαq“ΓRd上的有限正测度：|pΓptq|”OΓp|t|q，|t|ñ8(

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

Fourier decay for homogeneous self-affine measures

lim p μpξq “ 0, as |ξ| Ñ 8, where |ξ| is a norm (say, the Euclidean norm) of ξ P Rd. Whereas absolutely continuous measures are Rajchman by the Riemann-Lebesgue Lemma, it is a subtle question to decide which singular measures are such, see, e.g., the survey of Lyons [14]. A much stronger property, useful for many applications is the following. Definition 1.1. For α ą 0 let Ddpαq “ ν finite positive measure on Rd : |p νptq| “ Oνp|t|q, |t| Ñ 8 (

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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.