{"title":"平面自仿射测度的四元数字集正交指数","authors":"Hong Li","doi":"10.4208/jms.v55n3.22.07","DOIUrl":null,"url":null,"abstract":". Let µ M , D be a self-affine measure generated by an expanding real matrix M = (cid:18) a e f b (cid:19) and the digit set D = { ( 0,0 ) t , ( 1,0 ) t , ( 0,1 ) t , ( 1,1 ) t } . In this paper, we con-sider that when does L 2 ( µ M , D ) admit an infinite orthogonal set of exponential functions? Moreover, we obtain that if e = f = 0 and a , b ∈{ pq , p , q ∈ 2 Z + 1 } , then there exist at most 4 mutually orthogonal exponential functions in L 2 ( µ M , D ) , and the number 4 is the best possible.","PeriodicalId":43526,"journal":{"name":"数学研究","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Orthogonal Exponentials of Planar Self-Affine Measures with Four-Element Digit Set\",\"authors\":\"Hong Li\",\"doi\":\"10.4208/jms.v55n3.22.07\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". Let µ M , D be a self-affine measure generated by an expanding real matrix M = (cid:18) a e f b (cid:19) and the digit set D = { ( 0,0 ) t , ( 1,0 ) t , ( 0,1 ) t , ( 1,1 ) t } . In this paper, we con-sider that when does L 2 ( µ M , D ) admit an infinite orthogonal set of exponential functions? Moreover, we obtain that if e = f = 0 and a , b ∈{ pq , p , q ∈ 2 Z + 1 } , then there exist at most 4 mutually orthogonal exponential functions in L 2 ( µ M , D ) , and the number 4 is the best possible.\",\"PeriodicalId\":43526,\"journal\":{\"name\":\"数学研究\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2022-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"数学研究\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4208/jms.v55n3.22.07\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"数学研究","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4208/jms.v55n3.22.07","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
． 设µM, D是由展开实矩阵M = (cid:18) a e f b (cid:19)和数字集D = {(0,0) t， (1,0) t， (0,1) t， (1,1) t}生成的自仿射测度。在本文中，我们考虑l2(µM, D)在什么情况下允许一个指数函数的无限正交集?进一步得到，当e = f = 0，且a, b∈{pq, p, q∈2z + 1}，则l2(µM, D)中最多存在4个相互正交的指数函数，且4是最优值。
Orthogonal Exponentials of Planar Self-Affine Measures with Four-Element Digit Set
. Let µ M , D be a self-affine measure generated by an expanding real matrix M = (cid:18) a e f b (cid:19) and the digit set D = { ( 0,0 ) t , ( 1,0 ) t , ( 0,1 ) t , ( 1,1 ) t } . In this paper, we con-sider that when does L 2 ( µ M , D ) admit an infinite orthogonal set of exponential functions? Moreover, we obtain that if e = f = 0 and a , b ∈{ pq , p , q ∈ 2 Z + 1 } , then there exist at most 4 mutually orthogonal exponential functions in L 2 ( µ M , D ) , and the number 4 is the best possible.
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