A connection between multiresolution wavelet theory of scale \(N\) and representations of the Cuntz algebra \({\mathcal O}_N\). (English) Zbl 0915.46048
Doplicher, S. (ed.) et al., Operator algebras and quantum field theory. Proceedings of the conference dedicated to Daniel Kastler in celebration of his 70th birthday, Accademia Nazionale dei Lincei, Roma, Italy, July 1–6, 1996. Cambridge, MA: International Press. 151-163 (1997).
The article contains a survey of some results and open problems on the connection between wavelet theory on \(L^2(\mathbb{R})\) and certain representations of the Cuntz algebra on \(L^2(\mathbb{T})\). Complete proofs are given in two 1996 preprints by the authors and also in their recent paper [Integral Equations Oper. Theory 28, No. 4, 382-443 (1997; Zbl 0897.46054)].
For the entire collection see [Zbl 0889.00022].
For the entire collection see [Zbl 0889.00022].
Reviewer: Kh.N.Boyadzhiev (Ada)
MSC:
| 46L05 | General theory of \(C^*\)-algebras |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 46L55 | Noncommutative dynamical systems |
