Iterated function systems and permutation representations of the Cuntz algebra
| dc.creator | Bratteli, Ola | |
| dc.creator | Jorgensen, Palle E. T. | |
| dc.date | 1996-12-17 | |
| dc.date.accessioned | 2026-07-07T09:13:40Z | |
| dc.date.available | 2026-07-07T09:13:40Z | |
| dc.description | We study a class of representations of the Cuntz algebras O_N, N=2,3,..., acting on L^2(T) where T=R/2πZ. The representations arise in wavelet theory, but are of independent interest. We find and describe the decomposition into irreducibles, and show how the O_N-irreducibles decompose when restricted to the subalgebra UHF_N\subset O_N of gauge-invariant elements; and we show that the whole structure is accounted for by arithmetic and combinatorial properties of the integers Z. We have general results on a class of representations of O_N on Hilbert space H such that the generators S_i as operators permute the elements in some orthonormal basis for H. We then use this to extend our results from L^2(T) to L^2(T^d), d>1 ; even to L^2(\mathbf{T}) where \mathbf{T} is some fractal version of the torus which carries more of the algebraic information encoded in our representations. | |
| dc.description | 84 pages, 11 figures, AMS-LaTeX v1.2b, full-resolution figures available at ftp://ftp.math.uiowa.edu/pub/jorgen/PermRepCuntzAlg in eps files with the same names as the low-resolution figures included here | |
| dc.identifier | https://arxiv.org/abs/funct-an/9612002 | |
| dc.identifier | http://arxiv.org/abs/funct-an/9612002 | |
| dc.identifier | Mem. Amer. Math. Soc. 139 (1999), no. 663 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152405 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L55, 47C15 (Primary) 42C05, 22D25, 11B85 (Secondary) | |
| dc.title | Iterated function systems and permutation representations of the Cuntz algebra | |
| dc.type | text |