Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

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

Author(s): Eui-Chai Jeong
Journal: Proc. Amer. Math. Soc. 127 (1999), 3583-3590.
MSC (1991): Primary 46L30, 46L55, 46L89, 47A13, 47A67; Secondary 47A20, 47D25, 43A65
Posted: May 17, 1999
Retrieve article in: PDF DVI PostScript
This article is available free of charge

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.

References:

[BEEK]
Ola Bratteli, George A. Elliott, David E. Evans, and Akitaka Kishimoto, Quasi-product actions of a compact abelian group on a ${C}^{*}$-algebra, Tohoku Math. J. 41 (1989), 133-161. MR 90f:46103
[BraJo]
Ola Bratteli and Palle E.T. Jorgensen, Iterated function systems and permutation representations of the Cuntz algebra, Mem. Amer. Math. Soc., to appear. CMP 98:01
[BraJo97a]
Ola Bratteli and Palle E.T. Jorgensen, Endomorphisms of $\mathcal{B}(\mathcal{H})$, II: Finitely correlated states on $\mathcal{O}_{N}$, J. Funct. Anal. 145 (1997), 323-373. MR 98c:46128
[BraJo97b]
Ola Bratteli and Palle E.T. Jorgensen, Isometries, shifts, Cuntz algebras and multiresolution wavelet analysis of scale ${N}$, Integral Equations Operator Theory 28 (1997), 382-443. CMP 97:17
[BJP]
Ola Bratteli, Palle E.T. Jorgensen, and Geoffrey L. Price, Endomorphisms of $\mathcal{B}(\mathcal{H})$, Quantization, nonlinear partial differential equations, and operator algebra (William Arveson, Thomas Branson, and Irving Segal, eds.), Proc. Sympos. Pure Math., vol. 59, American Mathematical Society, 1996, pp. 93-138. MR 97h:46107
[CoRy]
Albert Cohen and Robert D. Ryan, Wavelets and multiscale signal processing, Applied Mathematics and Mathematical Computation, vol. 11, Chapman & Hall, London, 1995. MR 97k:42048

[Cun77]
Joachim Cuntz, Simple ${C}^{*}$ -algebras generated by isometries, Comm. Math. Phys. 57 (1977), 173-185. MR 57:7189
[Dau92]
Ingrid Daubechies, Ten lectures on wavelets, CBMS-NSF Regional Conf. Ser. in Appl. Math., vol. 61, Society for Industrial and Applied Mathematics, Philadelphia, 1992. MR 93e:42045
[JeongI]
Eui-Chai Jeong, Decomposition of Cuntz algebra representation, Ph.D. thesis, The University of Iowa, 1997.

[JeongII]
Eui-Chai Jeong, A number system in $\mathbb{R}^{n}$, Seoul National University, in preparation.

[Jor]
Palle E.T. Jorgensen, Harmonic analysis of fractal processes via ${C}^{\ast}$-algebras, Math. Nachr., to appear.

[JoPe94]
Palle E.T. Jorgensen and Steen Pedersen, Harmonic analysis and fractal limit-measures induced by representations of a certain ${C}^{\ast}$-algebra, J. Funct. Anal. 125 (1994), 90-110. MR 95i:47067
[JoPe96]
Palle E.T. Jorgensen and Steen Pedersen, Harmonic analysis of fractal measures, Constr. Approx. 12 (1996), 1-30. MR 97c:46091
[Pow88]
Robert T. Powers, An index theory for semigroups of ${}^{\ast}$-endomorphisms of $\mathcal{B}(\mathcal{H})$ and type $\mathrm{II}_{1}$ factors, Canad. J. Math. 40 (1988), 86-114. MR 89f:46116

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46L30, 46L55, 46L89, 47A13, 47A67, 47A20, 47D25, 43A65

Retrieve articles in all Journals with MSC (1991): 46L30, 46L55, 46L89, 47A13, 47A67, 47A20, 47D25, 43A65

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: 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
Posted: May 17, 1999
Communicated by: David R. Larson
Copyright of article: Copyright 1999, American Mathematical Society

Forward Citation(s):

Information for authors on submitting citations

The following works have cited this article

Eui-Chai Jeong, A simple slgebra generated by infinite isomrtries and representations, Comm. Korean Math. Soc. (1) 14 (1999), 157-169. (English) MR MR 2000d:46071

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google