Pure point dynamical and diffraction spectra

Annales Henri Poincare

Volumn 3, Issue 5, 2002, Pages 1003-1018

  Lee, J Y ^a   Moody, R V ^a   Solomyak, B ^b  

^a UNIVERSITY OF ALBERTA   (Canada)

^b UNIVERSITY OF WASHINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036435987     PISSN: 14240637     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00023-002-8646-1     Document Type: Article

References (17)

1. M. Baake and R.V. Moody, Weighted Dirac combs with pure point diffraction, math. MG/0203030, Preprint, 2002.
2. J. Chatard, Sur une généralisation du théorème de Birkhoff, C.R. Acad. Sc. Paris, t.275, Serie A, 1135-1138 (1972).
3. M. Denker, C. Grillenberger and K. Sigmund, Ergodic Theory on Compact Spaces, Springer Lecture Notes in Math. 527, Springer, 1976.
4. S. Dworkin, Spectral theory and X-ray diffraction, J. Math. Phys. 34, 2965-2967 (1993).
5. A.C.D. van Enter and J. Miȩkisz, How should one define a (weak) crystal? J. Stat. Phys. 66, 1147-1153 (1992).
6. A. Hof, Diffraction by aperiodic structures, in The Mathematics of Long-Range Aperiodic Order, (R.V. Moody, ed.), 239-268, Kluwer, 1997.
7. J.-Y. Lee and R.V. Moody, Lattice Substitution Systems and Model Sets. Discrete and Computational Geometry 25, 173-201 (2001).
8. J.-Y. Lee, R.V. Moody and B. Solomyak, Consequences of Pure Point Diffraction Spectra for Multiset Substitution Systems, Discrete and Computational Geometry (to appear), 2002.
9. E. Lindenstrauss, Pointwise theorems for amenable groups, Invent. Math. 146, 259-295 (2001).
10. G.W. Mackey, Unitary Group Representations in Physics, Probability, and Number Theory, Addison-Wesley, 1978,1989.
11. M. Queffelec, Substitution dynamical systems - spectral analysis, Springer Lecture Notes in Math. 1294, Springer, 1987.
12. C. Radin and M. Wolff, Space tilings and local isomorphism, Geometriae Dedicata 42, 355-360 (1992).
13. M. Schlottmann, Generalized model sets and dynamical systems, in: Directions in Mathematical Quasicrystals, eds. M. Baake and R.V. Moody, CRM Monograph series, AMS, Providence RI (2000), 143-159.
14. B. Solomyak, Dynamics of self-similar tilings, Ergodic Th. Dynam. Sys. 17, 695-738 (1997).
15. A.A. Tempel'man, Ergodic theorems for general dynamical systems, Dokl. Akad. Nauk SSSR, vol. 176 (1967), no. 4, 790-793 (English translation: Soviet Math. Dokl., vol. 8 (1967), no. 5, 1213-1216).
16. P. Walters, An introduction to ergodic theory, Springer Graduate Texts in Mathematics, Springer-Verlag, New York, 1982.
17. J. Weidmann, Linear Operators in Hilbert Space, Springer Graduate Texts in Mathematics, Springer-Verlag, New York, 1980.