KMS Of Academy of mathematics and systems sciences, CAS
Boundedness and Spectrum of Multiplicative Convolution Operators Induced by Arithmetic Functions | |
Gebremeskel, Kibrom G.1,2; Huang, Lin Zhe1 | |
2019-08-01 | |
Source Publication | ACTA MATHEMATICA SINICA-ENGLISH SERIES |
ISSN | 1439-8516 |
Volume | 35Issue:8Pages:1300-1310 |
Abstract | 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 |
Keyword | Arithmetic functions Mobius function von Neumann algebra |
DOI | 10.1007/s10114-019-8329-1 |
Language | 英语 |
Funding Project | Templeton Religion Trust[TRT 0159] ; Chinese Academy of Sciences |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000476705300002 |
Publisher | SPRINGER HEIDELBERG |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/35364 |
Collection | 中国科学院数学与系统科学研究院 |
Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Aksum Univ, Coll Nat & Computat Sci, Dept Math, Aksum, Tigray, Ethiopia |
Recommended Citation 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. |
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