{"title":"方形白噪声李代数的q-变形","authors":"Sami H. Altoum","doi":"10.1016/j.trmi.2018.01.005","DOIUrl":null,"url":null,"abstract":"<div><p>For <span><math><mi>q</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math></span>, the <span><math><mi>q</mi></math></span>-deformation of the square white noise Lie algebra is introduced using the <span><math><mi>q</mi></math></span>-calculus. A representation of this Lie algebra is given, using the <span><math><mi>q</mi></math></span>-derivative (or Jackson derivative) and the multiplication operator. The free square white noise Lie algebra is defined. Moreover, its representation on the Hardy space is given.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"172 2","pages":"Pages 133-139"},"PeriodicalIF":0.3000,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2018.01.005","citationCount":"3","resultStr":"{\"title\":\"q-deformation of the square white noise Lie algebra\",\"authors\":\"Sami H. Altoum\",\"doi\":\"10.1016/j.trmi.2018.01.005\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>For <span><math><mi>q</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math></span>, the <span><math><mi>q</mi></math></span>-deformation of the square white noise Lie algebra is introduced using the <span><math><mi>q</mi></math></span>-calculus. A representation of this Lie algebra is given, using the <span><math><mi>q</mi></math></span>-derivative (or Jackson derivative) and the multiplication operator. The free square white noise Lie algebra is defined. Moreover, its representation on the Hardy space is given.</p></div>\",\"PeriodicalId\":43623,\"journal\":{\"name\":\"Transactions of A Razmadze Mathematical Institute\",\"volume\":\"172 2\",\"pages\":\"Pages 133-139\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2018-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.trmi.2018.01.005\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions of A Razmadze Mathematical Institute\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2346809217301526\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of A Razmadze Mathematical Institute","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2346809217301526","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
q-deformation of the square white noise Lie algebra
For , the -deformation of the square white noise Lie algebra is introduced using the -calculus. A representation of this Lie algebra is given, using the -derivative (or Jackson derivative) and the multiplication operator. The free square white noise Lie algebra is defined. Moreover, its representation on the Hardy space is given.