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Boundedness and Spectrum of Multiplicative Convolution Operators Induced by Arithmetic Functions
Gebremeskel, Kibrom G.1,2; Huang, Lin Zhe1
2019-08-01
Source PublicationACTA MATHEMATICA SINICA-ENGLISH SERIES
ISSN1439-8516
Volume35Issue:8Pages:1300-1310
AbstractIn 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 muM mu. Moreover, von Neumann algebra generated by a certain family of bounded operators is also considered.
KeywordArithmetic functions Mobius function von Neumann algebra
DOI10.1007/s10114-019-8329-1
Language英语
Funding ProjectTempleton Religion Trust[TRT 0159] ; Chinese Academy of Sciences
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000476705300002
PublisherSPRINGER HEIDELBERG
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/35364
Collection中国科学院数学与系统科学研究院
Corresponding AuthorGebremeskel, Kibrom G.
Affiliation1.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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