{"title":"论具有广义几何权重的加权移位算子的数值半径","authors":"Bikshan Chakraborty, Sarita Ojha","doi":"10.1016/j.jmaa.2024.129021","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we give bounds on the numerical radius of the weighted shift operator <em>T</em> with generalized geometric weights<span><span><span><math><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mi>s</mi><mi>q</mi><mo>,</mo><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mi>s</mi><msup><mrow><mi>q</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo><mo>…</mo><mo>,</mo><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn><mi>n</mi><mo>−</mo><mn>2</mn></mrow></msup><mo>,</mo><mi>s</mi><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>,</mo><mo>…</mo><mo>)</mo></mrow><mo>,</mo></math></span></span></span> where <span><math><mi>s</mi><mo>></mo><mn>0</mn></math></span> and <span><math><mn>0</mn><mo><</mo><mi>q</mi><mo><</mo><mn>1</mn></math></span>. Also, we provide the entire function <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></span> whose minimal positive root gives the numerical radius of the weighted shift operator <em>T</em>. The purpose of this paper is to generalize the results of numerical radius for the weighted shift operator with geometric weights given in <span><span>[5]</span></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129021"},"PeriodicalIF":1.2000,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the numerical radius of weighted shift operators with generalized geometric weights\",\"authors\":\"Bikshan Chakraborty, Sarita Ojha\",\"doi\":\"10.1016/j.jmaa.2024.129021\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we give bounds on the numerical radius of the weighted shift operator <em>T</em> with generalized geometric weights<span><span><span><math><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mi>s</mi><mi>q</mi><mo>,</mo><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mi>s</mi><msup><mrow><mi>q</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo><mo>…</mo><mo>,</mo><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn><mi>n</mi><mo>−</mo><mn>2</mn></mrow></msup><mo>,</mo><mi>s</mi><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>,</mo><mo>…</mo><mo>)</mo></mrow><mo>,</mo></math></span></span></span> where <span><math><mi>s</mi><mo>></mo><mn>0</mn></math></span> and <span><math><mn>0</mn><mo><</mo><mi>q</mi><mo><</mo><mn>1</mn></math></span>. Also, we provide the entire function <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></span> whose minimal positive root gives the numerical radius of the weighted shift operator <em>T</em>. The purpose of this paper is to generalize the results of numerical radius for the weighted shift operator with geometric weights given in <span><span>[5]</span></span>.</div></div>\",\"PeriodicalId\":50147,\"journal\":{\"name\":\"Journal of Mathematical Analysis and Applications\",\"volume\":\"543 2\",\"pages\":\"Article 129021\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-11-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Analysis and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022247X24009430\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X24009430","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
本文给出了具有广义几何权重(1,sq,q2,sq3,...,q2n-2,sq2n-1,...)(其中 s>0 和 0<q<1)的加权移位算子 T 的数值半径边界。此外,我们还提供了整个函数 FT(z),其最小正根给出了加权移位算子 T 的数值半径。本文的目的是推广 [5] 中给出的具有几何权重的加权移位算子的数值半径结果。
On the numerical radius of weighted shift operators with generalized geometric weights
In this paper, we give bounds on the numerical radius of the weighted shift operator T with generalized geometric weights where and . Also, we provide the entire function whose minimal positive root gives the numerical radius of the weighted shift operator T. The purpose of this paper is to generalize the results of numerical radius for the weighted shift operator with geometric weights given in [5].
期刊介绍:
The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions.
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