{"title":"关于自由单一布朗运动被自由投影压缩的星矩","authors":"N. Demni, Tarek Hamdi","doi":"10.7900/jot.2020oct06.2319","DOIUrl":null,"url":null,"abstract":"In this paper, we derive explicit expressions for some classes of ⋆-moments of a free unitary Brownian motion compressed by a free projection, using various methods. While the moments of this nonnormal operator are readily derived through analytical or combinatorial methods, we only succeeded to derive its mixed ones after solving a nonlinear partial differential equation (pde) for their generating function. We shall also give some interest in odd alternating moments. In particular, we derive a linear pde for their generating function which we solve when the rank of the projection equals~1/2.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2020-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On star moments of the compression of the free unitary Brownian motion by a free projection\",\"authors\":\"N. Demni, Tarek Hamdi\",\"doi\":\"10.7900/jot.2020oct06.2319\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we derive explicit expressions for some classes of ⋆-moments of a free unitary Brownian motion compressed by a free projection, using various methods. While the moments of this nonnormal operator are readily derived through analytical or combinatorial methods, we only succeeded to derive its mixed ones after solving a nonlinear partial differential equation (pde) for their generating function. We shall also give some interest in odd alternating moments. In particular, we derive a linear pde for their generating function which we solve when the rank of the projection equals~1/2.\",\"PeriodicalId\":50104,\"journal\":{\"name\":\"Journal of Operator Theory\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2020-01-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Operator Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.7900/jot.2020oct06.2319\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Operator Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7900/jot.2020oct06.2319","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
On star moments of the compression of the free unitary Brownian motion by a free projection
In this paper, we derive explicit expressions for some classes of ⋆-moments of a free unitary Brownian motion compressed by a free projection, using various methods. While the moments of this nonnormal operator are readily derived through analytical or combinatorial methods, we only succeeded to derive its mixed ones after solving a nonlinear partial differential equation (pde) for their generating function. We shall also give some interest in odd alternating moments. In particular, we derive a linear pde for their generating function which we solve when the rank of the projection equals~1/2.
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The Journal of Operator Theory is rigorously peer reviewed and endevours to publish significant articles in all areas of operator theory, operator algebras and closely related domains.
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