Boundedness and Spectrum of Multiplicative Convolution Operators Induced by Arithmetic Functions
文献类型：期刊论文
| 作者 | Gebremeskel, Kibrom G.1,2; Huang, Lin Zhe2 |
| 刊名 | ACTA MATHEMATICA SINICA-ENGLISH SERIES
 |
| 出版日期 | 2019-08-01 |
| 卷号 | 35期号:8页码:1300-1310 |
| 关键词 | Arithmetic functions Mobius function von Neumann algebra |
| ISSN号 | 1439-8516 |
| DOI | 10.1007/s10114-019-8329-1 |
| 英文摘要 | In this paper, we consider a multiplicative convolution operator Mf acting on a Hilbert spaces l(2)(N,omega). In particular, we focus on the operators M1 and M mu, where mu is the Mobius function. We investigate conditions on the weight omega under which the operators M1 and M mu 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 parallel to f parallel to(1) < infinity, in which case parallel to M-1 parallel to(2),omega = parallel to f parallel to(1), where w(n) = f(2)(n). Analogously, we show that is bounded on l(2)(N,1/n(2 alpha)) with M mu 2,omega= zeta(alpha)zeta(2 alpha) , where omega(n) = 1/n(2 alpha), alpha > 1. As an application, we obtain some results on the spectrum of M1 M1 and M mu |
| 资助项目 | Templeton Religion Trust[TRT 0159] ; Chinese Academy of Sciences |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000476705300002 |
| 出版者 | SPRINGER HEIDELBERG |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/35363]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Gebremeskel, Kibrom G. |
| 作者单位 | 1.Aksum Univ, Coll Nat & Computat Sci, Dept Math, Aksum, Tigray, Ethiopia 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Gebremeskel, Kibrom G.,Huang, Lin Zhe. Boundedness and Spectrum of Multiplicative Convolution Operators Induced by Arithmetic Functions[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES,2019,35(8):1300-1310. |
| APA | Gebremeskel, Kibrom G.,&Huang, Lin Zhe.(2019).Boundedness and Spectrum of Multiplicative Convolution Operators Induced by Arithmetic Functions.ACTA MATHEMATICA SINICA-ENGLISH SERIES,35(8),1300-1310. |
| MLA | Gebremeskel, Kibrom G.,et al."Boundedness and Spectrum of Multiplicative Convolution Operators Induced by Arithmetic Functions".ACTA MATHEMATICA SINICA-ENGLISH SERIES 35.8(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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