{"title":"Pure Point Diffraction and Almost Periodicity","authors":"Daniel Lenz, Timo Spindeler, Nicolae Strungaru","doi":"10.1002/ijch.202300158","DOIUrl":null,"url":null,"abstract":"<p>This article deals with pure point diffraction and its connection to various notions of almost periodicity. We explain why the Fibonacci chain does not fit into the classical concept of Bohr almost periodicity and how it fits into the classes of mean, Besicovitch and Weyl almost periodic point sets. We report on recent results which characterize pure point diffraction as mean almost periodicity of the underlying structure, and discuss how the complex amplitudes fit into this picture.</p>","PeriodicalId":14686,"journal":{"name":"Israel Journal of Chemistry","volume":"64 10-11","pages":""},"PeriodicalIF":2.3000,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/ijch.202300158","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Israel Journal of Chemistry","FirstCategoryId":"92","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/ijch.202300158","RegionNum":4,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
This article deals with pure point diffraction and its connection to various notions of almost periodicity. We explain why the Fibonacci chain does not fit into the classical concept of Bohr almost periodicity and how it fits into the classes of mean, Besicovitch and Weyl almost periodic point sets. We report on recent results which characterize pure point diffraction as mean almost periodicity of the underlying structure, and discuss how the complex amplitudes fit into this picture.
期刊介绍：
The fledgling State of Israel began to publish its scientific activity in 1951 under the general heading of Bulletin of the Research Council of Israel, which quickly split into sections to accommodate various fields in the growing academic community. In 1963, the Bulletin ceased publication and independent journals were born, with Section A becoming the new Israel Journal of Chemistry.
The Israel Journal of Chemistry is the official journal of the Israel Chemical Society. Effective from Volume 50 (2010) it is published by Wiley-VCH.
The Israel Journal of Chemistry is an international and peer-reviewed publication forum for Special Issues on timely research topics in all fields of chemistry: from biochemistry through organic and inorganic chemistry to polymer, physical and theoretical chemistry, including all interdisciplinary topics. Each topical issue is edited by one or several Guest Editors and primarily contains invited Review articles. Communications and Full Papers may be published occasionally, if they fit with the quality standards of the journal. The publication language is English and the journal is published twelve times a year.
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