{"title":"海森堡运动群的不确定性原理","authors":"Walid Amghar","doi":"10.1155/2021/3734817","DOIUrl":null,"url":null,"abstract":"<jats:p>In this article, we will recall the main properties of the Fourier transform on the Heisenberg motion group <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\n <mi>G</mi>\n <mo>=</mo>\n <msup>\n <mrow>\n <mi>ℍ</mi>\n </mrow>\n <mrow>\n <mi>n</mi>\n </mrow>\n </msup>\n <mo>⋊</mo>\n <mi>K</mi>\n </math>\n </jats:inline-formula>, where <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\n <mi>K</mi>\n <mo>=</mo>\n <mi>U</mi>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <mi>n</mi>\n </mrow>\n </mfenced>\n </math>\n </jats:inline-formula> and <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\n <msup>\n <mrow>\n <mi>ℍ</mi>\n </mrow>\n <mrow>\n <mi>n</mi>\n </mrow>\n </msup>\n <mo>=</mo>\n <msup>\n <mrow>\n <mi>ℂ</mi>\n </mrow>\n <mrow>\n <mi>n</mi>\n </mrow>\n </msup>\n <mo>×</mo>\n <mi>ℝ</mi>\n </math>\n </jats:inline-formula> denote the Heisenberg group. Then, we will present some uncertainty principles associated to this transform as Beurling, Hardy, and Gelfand-Shilov.</jats:p>","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Uncertainty Principles for Heisenberg Motion Group\",\"authors\":\"Walid Amghar\",\"doi\":\"10.1155/2021/3734817\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<jats:p>In this article, we will recall the main properties of the Fourier transform on the Heisenberg motion group <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M1\\\">\\n <mi>G</mi>\\n <mo>=</mo>\\n <msup>\\n <mrow>\\n <mi>ℍ</mi>\\n </mrow>\\n <mrow>\\n <mi>n</mi>\\n </mrow>\\n </msup>\\n <mo>⋊</mo>\\n <mi>K</mi>\\n </math>\\n </jats:inline-formula>, where <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M2\\\">\\n <mi>K</mi>\\n <mo>=</mo>\\n <mi>U</mi>\\n <mfenced open=\\\"(\\\" close=\\\")\\\">\\n <mrow>\\n <mi>n</mi>\\n </mrow>\\n </mfenced>\\n </math>\\n </jats:inline-formula> and <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M3\\\">\\n <msup>\\n <mrow>\\n <mi>ℍ</mi>\\n </mrow>\\n <mrow>\\n <mi>n</mi>\\n </mrow>\\n </msup>\\n <mo>=</mo>\\n <msup>\\n <mrow>\\n <mi>ℂ</mi>\\n </mrow>\\n <mrow>\\n <mi>n</mi>\\n </mrow>\\n </msup>\\n <mo>×</mo>\\n <mi>ℝ</mi>\\n </math>\\n </jats:inline-formula> denote the Heisenberg group. Then, we will present some uncertainty principles associated to this transform as Beurling, Hardy, and Gelfand-Shilov.</jats:p>\",\"PeriodicalId\":7061,\"journal\":{\"name\":\"Abstract and Applied Analysis\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-11-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Abstract and Applied Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/2021/3734817\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Abstract and Applied Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2021/3734817","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
Uncertainty Principles for Heisenberg Motion Group
In this article, we will recall the main properties of the Fourier transform on the Heisenberg motion group , where and denote the Heisenberg group. Then, we will present some uncertainty principles associated to this transform as Beurling, Hardy, and Gelfand-Shilov.
期刊介绍:
Abstract and Applied Analysis is a mathematical journal devoted exclusively to the publication of high-quality research papers in the fields of abstract and applied analysis. Emphasis is placed on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, optimization theory, and control theory. Abstract and Applied Analysis supports the publication of original material involving the complete solution of significant problems in the above disciplines. Abstract and Applied Analysis also encourages the publication of timely and thorough survey articles on current trends in the theory and applications of analysis.