{"title":"R2 上一类随机卷积光谱的贝林维度","authors":"Jinjun Li, Zhiyi Wu","doi":"10.1016/j.acha.2024.101683","DOIUrl":null,"url":null,"abstract":"<div><p>It is usually difficult to study the structure of the spectra for the measures in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and higher dimensions. In this paper, by employing the projective techniques and our previous results on the line we prove that the Beurling dimension of spectra for a class of random convolutions in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> satisfies an intermediate value property.</p></div>","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"73 ","pages":"Article 101683"},"PeriodicalIF":2.6000,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Beurling dimension of spectra for a class of random convolutions on R2\",\"authors\":\"Jinjun Li, Zhiyi Wu\",\"doi\":\"10.1016/j.acha.2024.101683\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>It is usually difficult to study the structure of the spectra for the measures in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and higher dimensions. In this paper, by employing the projective techniques and our previous results on the line we prove that the Beurling dimension of spectra for a class of random convolutions in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> satisfies an intermediate value property.</p></div>\",\"PeriodicalId\":55504,\"journal\":{\"name\":\"Applied and Computational Harmonic Analysis\",\"volume\":\"73 \",\"pages\":\"Article 101683\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2024-07-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied and Computational Harmonic Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1063520324000605\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied and Computational Harmonic Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1063520324000605","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Beurling dimension of spectra for a class of random convolutions on R2
It is usually difficult to study the structure of the spectra for the measures in and higher dimensions. In this paper, by employing the projective techniques and our previous results on the line we prove that the Beurling dimension of spectra for a class of random convolutions in satisfies an intermediate value property.
期刊介绍：
Applied and Computational Harmonic Analysis (ACHA) is an interdisciplinary journal that publishes high-quality papers in all areas of mathematical sciences related to the applied and computational aspects of harmonic analysis, with special emphasis on innovative theoretical development, methods, and algorithms, for information processing, manipulation, understanding, and so forth. The objectives of the journal are to chronicle the important publications in the rapidly growing field of data representation and analysis, to stimulate research in relevant interdisciplinary areas, and to provide a common link among mathematical, physical, and life scientists, as well as engineers.
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