{"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}
引用次数: 3
Abstract
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.
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