Irreducible representations of the Cuntz algebra
Author:
EuiChai Jeong
Journal:
Proc. Amer. Math. Soc. 127 (1999), 35833590
MSC (1991):
Primary 46L30, 46L55, 46L89, 47A13, 47A67; Secondary 47A20, 47D25, 43A65
Published electronically:
May 17, 1999
MathSciNet review:
1621953
Fulltext PDF Free Access
Abstract 
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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 , . These irreducible representations arise as subrepresentations of naturally occurring representations of acting in and arise from consideration of multiresolution wavelet filters.
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 Ola Bratteli, George A. Elliott, David E. Evans, and Akitaka Kishimoto, Quasiproduct actions of a compact abelian group on a algebra, Tohoku Math. J. 41 (1989), 133161. 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 , II: Finitely correlated states on , J. Funct. Anal. 145 (1997), 323373. MR 98c:46128
 [BraJo97b]
 Ola Bratteli and Palle E.T. Jorgensen, Isometries, shifts, Cuntz algebras and multiresolution wavelet analysis of scale , Integral Equations Operator Theory 28 (1997), 382443. CMP 97:17
 [BJP]
 Ola Bratteli, Palle E.T. Jorgensen, and Geoffrey L. Price, Endomorphisms of , 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. 93138. 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
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 Joachim Cuntz, Simple algebras generated by isometries, Comm. Math. Phys. 57 (1977), 173185. MR 57:7189
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 Ingrid Daubechies, Ten lectures on wavelets, CBMSNSF Regional Conf. Ser. in Appl. Math., vol. 61, Society for Industrial and Applied Mathematics, Philadelphia, 1992. MR 93e:42045
 [JeongI]
 EuiChai Jeong, Decomposition of Cuntz algebra representation, Ph.D. thesis, The University of Iowa, 1997.
 [JeongII]
 EuiChai Jeong, A number system in , Seoul National University, in preparation.
 [Jor]
 Palle E.T. Jorgensen, Harmonic analysis of fractal processes via algebras, Math. Nachr., to appear.
 [JoPe94]
 Palle E.T. Jorgensen and Steen Pedersen, Harmonic analysis and fractal limitmeasures induced by representations of a certain algebra, J. Funct. Anal. 125 (1994), 90110. MR 95i:47067
 [JoPe96]
 Palle E.T. Jorgensen and Steen Pedersen, Harmonic analysis of fractal measures, Constr. Approx. 12 (1996), 130. MR 97c:46091
 [Pow88]
 Robert T. Powers, An index theory for semigroups of endomorphisms of and type factors, Canad. J. Math. 40 (1988), 86114. MR 89f:46116
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Additional Information
EuiChai Jeong
Affiliation:
Department of Mathematics, College of Natural Sciences, Seoul National University, Seoul 151742, Korea
Email:
jeong@cau.ac.kr
DOI:
http://dx.doi.org/10.1090/S0002993999050182
PII:
S 00029939(99)050182
Keywords:
$C^{\ast}$\nobreakdashalgebra,
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
