Boundedness and Spec trum of Multiplicative Convolution Operators Induced by Arithmetic Functions
文献类型：期刊论文
| 作者 | Kibrom GEBREMESKEL1; Lin Zhe HUANG1 |
| 刊名 | 数学学报:英文版
 |
| 出版日期 | 2019 |
| 卷号 | 35.0期号:008页码:1300-1310 |
| 关键词 | Arithmetic functions Mobius function von Neumann algebra |
| ISSN号 | 1439-8516 |
| 其他题名 | Boundedness and Spectrum of Multiplicative Convolution Operators Induced by Arithmetic Functions |
| 英文摘要 | In this paper, we consider a multiplicative convolution operator Mf acting on a Hilbert spaces l^2(N,ω;). In particular, we focus on the operators M1 and Mμ, where μ, is the Mobius function. We investigate conditions on the weight ω under which the operators M1 and Mμ are bounded. We show that for a positive and completely multiplicative function f,M1 is bounded on l^2(N, f^2) if and only if ||f||1 1. As an application, we obtain some results on the spectrum of M1^*M1 and M^*μMμ. Moreover, von Neumann algebra generated by a certain family of bounded operators is also considered. |
| 资助项目 | [Templeton Religion Trust] ; [Chinese Academy of Sciences] |
| 语种 | 中文 |
| CSCD记录号 | CSCD:6538831 |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/55458]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 作者单位 | 1.中国科学院数学与系统科学研究院 2.Department of Mathematics, College of Natural and Computational Sciences, Aksum University, Aksum, Tigray, Ethiopia |
| 推荐引用方式 GB/T 7714 | Kibrom GEBREMESKEL,Lin Zhe HUANG. Boundedness and Spec trum of Multiplicative Convolution Operators Induced by Arithmetic Functions[J]. 数学学报:英文版,2019,35.0(008):1300-1310. |
| APA | Kibrom GEBREMESKEL,&Lin Zhe HUANG.(2019).Boundedness and Spec trum of Multiplicative Convolution Operators Induced by Arithmetic Functions.数学学报:英文版,35.0(008),1300-1310. |
| MLA | Kibrom GEBREMESKEL,et al."Boundedness and Spec trum of Multiplicative Convolution Operators Induced by Arithmetic Functions".数学学报:英文版 35.0.008(2019):1300-1310. |
入库方式： OAI收割
来源：数学与系统科学研究院
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