{"title":"域上的正交傅里叶分析","authors":"Mihail N. Kolountzakis","doi":"arxiv-2408.15361","DOIUrl":null,"url":null,"abstract":"In this paper we go over the history of the Fuglede or Spectral Set\nConjecture as it has developed over the last 30 years or so. We do not aim to\nbe exhaustive and we do not cover important areas of development such as the\nresults on the problem in classes of finite groups or the version of the\nproblem that focuses on spectral measures instead of sets. The selection of the\nmaterial has been strongly influenced by personal taste, history and\ncapabilities. We are trying to be more descriptive than detailed and we point\nout several open questions.","PeriodicalId":501444,"journal":{"name":"arXiv - MATH - Metric Geometry","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Orthogonal Fourier Analysis on Domains\",\"authors\":\"Mihail N. Kolountzakis\",\"doi\":\"arxiv-2408.15361\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we go over the history of the Fuglede or Spectral Set\\nConjecture as it has developed over the last 30 years or so. We do not aim to\\nbe exhaustive and we do not cover important areas of development such as the\\nresults on the problem in classes of finite groups or the version of the\\nproblem that focuses on spectral measures instead of sets. The selection of the\\nmaterial has been strongly influenced by personal taste, history and\\ncapabilities. We are trying to be more descriptive than detailed and we point\\nout several open questions.\",\"PeriodicalId\":501444,\"journal\":{\"name\":\"arXiv - MATH - Metric Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Metric Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.15361\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Metric Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.15361","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper we go over the history of the Fuglede or Spectral Set
Conjecture as it has developed over the last 30 years or so. We do not aim to
be exhaustive and we do not cover important areas of development such as the
results on the problem in classes of finite groups or the version of the
problem that focuses on spectral measures instead of sets. The selection of the
material has been strongly influenced by personal taste, history and
capabilities. We are trying to be more descriptive than detailed and we point
out several open questions.
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