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2014 Actions of arithmetic functions on matrices and corresponding representations
Ilwoo Cho, Palle Jorgensen
Ann. Funct. Anal. 5(2): 90-117 (2014). DOI: 10.15352/afa/1396833506

Abstract

In this paper, we study a class of representations of arithmetic functions, and corresponding operator-theoretic and free probabilistic properties. We associate given arithmetic functions $f$ to certain matrices $\alpha _{n}(f).$

Citation

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Ilwoo Cho. Palle Jorgensen. "Actions of arithmetic functions on matrices and corresponding representations." Ann. Funct. Anal. 5 (2) 90 - 117, 2014. https://doi.org/10.15352/afa/1396833506

Information

Published: 2014
First available in Project Euclid: 7 April 2014

zbMATH: 1309.46037
MathSciNet: MR3192013
Digital Object Identifier: 10.15352/afa/1396833506

Subjects:
Primary: 46L53
Secondary: 05E15 , 11G15 , 11R04 , 11R09 , 11R47 , 11R56 , 46L10 , 46L40 , 46L54 , 47L15 , 47L30 , 47L55

Keywords: arithmetic algebra , Arithmetic function , arithmetic prime probability space , convolution operator , Krein space , linear functional , multiplication operator , representation

Rights: Copyright © 2014 Tusi Mathematical Research Group

Vol.5 • No. 2 • 2014
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