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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Irreducible representations
of the Cuntz algebra $\mathcal{O}_{N}$


Author: Eui-Chai Jeong
Journal: Proc. Amer. Math. Soc. 127 (1999), 3583-3590
MSC (1991): Primary 46L30, 46L55, 46L89, 47A13, 47A67; Secondary 47A20, 47D25, 43A65
Published electronically: May 17, 1999
MathSciNet review: 1621953
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we establish formulas for the configuration of a special class of irreducible representations of the Cuntz algebra $\mathcal{O}_{N}$, $N=2,3,\dots,\infty$. These irreducible representations arise as subrepresentations of naturally occurring representations of $\mathcal{O}_{N}$ acting in $L^{2}\left( \mathbb{T}\right) $ and arise from consideration of multiresolution wavelet filters.


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Additional Information

Eui-Chai Jeong
Affiliation: Department of Mathematics, College of Natural Sciences, Seoul National University, Seoul 151-742, Korea
Email: jeong@cau.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05018-2
PII: S 0002-9939(99)05018-2
Keywords: $C^{\ast}$\nobreakdash-algebra, wavelet, irreducible representation
Received by editor(s): February 16, 1998
Published electronically: May 17, 1999
Communicated by: David R. Larson
Article copyright: © Copyright 1999 American Mathematical Society