{"title":"非 Kac 紧凑量子群上中心傅里叶级数的 Khintchine 不等式","authors":"Sang-Gyun Youn","doi":"arxiv-2408.13519","DOIUrl":null,"url":null,"abstract":"The study of Khintchin inequalities has a long history in abstract harmonic\nanalysis. While there is almost no possibility of non-trivial Khintchine\ninequality for central Fourier series on compact connected semisimple Lie\ngroups, we demonstrate a strong contrast within the framework of compact\nquantum groups. Specifically, we establish a Khintchine inequality with\noperator coefficients for arbitrary central Fourier series in a large class of\nnon-Kac compact quantum groups. The main examples include the Drinfeld-Jimbo\n$q$-deformations $G_q$, the free orthogonal quantum groups $O_F^+$, and the\nquantum automorphism group $G_{aut}(B,\\psi)$ with a $\\delta$-form $\\psi$.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":"12 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Khintchine inequality for central Fourier series on non-Kac compact quantum groups\",\"authors\":\"Sang-Gyun Youn\",\"doi\":\"arxiv-2408.13519\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The study of Khintchin inequalities has a long history in abstract harmonic\\nanalysis. While there is almost no possibility of non-trivial Khintchine\\ninequality for central Fourier series on compact connected semisimple Lie\\ngroups, we demonstrate a strong contrast within the framework of compact\\nquantum groups. Specifically, we establish a Khintchine inequality with\\noperator coefficients for arbitrary central Fourier series in a large class of\\nnon-Kac compact quantum groups. The main examples include the Drinfeld-Jimbo\\n$q$-deformations $G_q$, the free orthogonal quantum groups $O_F^+$, and the\\nquantum automorphism group $G_{aut}(B,\\\\psi)$ with a $\\\\delta$-form $\\\\psi$.\",\"PeriodicalId\":501114,\"journal\":{\"name\":\"arXiv - MATH - Operator Algebras\",\"volume\":\"12 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Operator Algebras\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.13519\",\"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 - Operator Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.13519","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Khintchine inequality for central Fourier series on non-Kac compact quantum groups
The study of Khintchin inequalities has a long history in abstract harmonic
analysis. While there is almost no possibility of non-trivial Khintchine
inequality for central Fourier series on compact connected semisimple Lie
groups, we demonstrate a strong contrast within the framework of compact
quantum groups. Specifically, we establish a Khintchine inequality with
operator coefficients for arbitrary central Fourier series in a large class of
non-Kac compact quantum groups. The main examples include the Drinfeld-Jimbo
$q$-deformations $G_q$, the free orthogonal quantum groups $O_F^+$, and the
quantum automorphism group $G_{aut}(B,\psi)$ with a $\delta$-form $\psi$.