Iterated Function Systems and Permutation Representations of the Cuntz Algebra.

Intro -- Contents -- List of Figures -- Chapter 1. Introduction -- Chapter 2. Permutative representations of O[sub(N)] -- Chapter 3. Monomial representations and integers modulo N -- Chapter 4. Cycles of irreducible O[sub(N)] representations and their atoms of UHF[sub(N)] representations -- Chapter 5. Relations of finite type and sub-Cuntz states -- Chapter 6. The shift representation -- Chapter 7. The universal permutative multiplicity-free representation -- Chapter 8. Some specific examples of the cycle and atom structure: The mod N case -- 8.1. The case N = 2 -- 8.2. The case N general, s[sub(i)] = i for i ε z[sub(N)] = {0,1,...,N…1} -- 8.3. The case N = 3, {s[sub(i)]} = {1,3,5} -- Chapter 9. Some specific examples of the cycle and atom structure: The mod N case -- 9.1. A matrix case -- 9.2. Another matrix case: full spectrum -- 9.3. Self-similarity and tiles -- 9.4. Tiles in the plane -- 9.5. Single-atom cases -- 9.6. Multiple coverings -- 9.7. Box spline matrices -- Chapter 10. The general mod N situation -- Chapter 11. Concluding remarks -- Bibliography -- List of Symbols.

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