Consequences of pure point diffraction spectra for multiset substitution systems

Discrete and Computational Geometry

Volumn 29, Issue 4, 2003, Pages 525-560

  Lee, Jeong Yup ^a   Moody, Robert V ^a   Solomyak, Boris ^b  

^a UNIVERSITY OF ALBERTA   (Canada)

^b UNIVERSITY OF WASHINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038169056     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00454-003-0781-z     Document Type: Article

References (19)

1. M. Baake and R. V. Moody, Self-similar measures for quasi-crystals, in Directions in Mathematical Quasicrystals, M. Baake and R. V. Moody, eds., CRM Monograph Series, Vol. 13, AMS, Providence, RI, 2000, pp. 1-42.
2. M. Baake and R. V. Moody, Weighted Dirac combs with pure point diffraction, Preprint, 2002.
3. L. Danzer, Inflation-species of planar tilings which are not of locally finite complexity, Proc. Steklov Inst. Math. 239 (2002), 1-9.
4. M. Dekking, The spectrum of dynamical systems arising from substitutions of constant length, Z. Wahrsch. Verw. Gebiete 41 (1978), 221-239.
5. S. Dworkin, Spectral theory and X-ray diffraction, J. Math. Phys. 34 (1993), 2965-2967.
6. H. Furstenberg, Recurrence in Ergodic Theory and Combinatorial Number Theory, Princeton University Press, Princeton, NJ, 1981.
7. C. P. M. Geerse and A. Hof, Lattice gas models on self-similar aperiodic tilings, Rev. Math. Phys. 3 (1991), 163-221.
8. A. Hof, Diffraction by aperiodic structures, in The Mathematics of Long-Range Aperiodic Order, R. V. Moody, ed., Kluwer, Dordrecht, 1997, pp. 239-268,
9. J. C. Lagarias and Y. Wang, Substitution Delone sets, Discrete Comput. Geom. 29 (2003), 175-209.
10. J.-Y. Lee and R. V. Moody, Lattice substitution systems and model sets, Discrete Comput. Geom. 25 (2001), 173-201.
11. J.-Y. Lee, R. V. Moody, and B. Solomyak, Pure point dynamical and diffraction spectra, Ann. Henri Poincaré 3 (2002), 1003-1018.
12. R. V. Moody, Model sets: a survey, in From Quasicrystals to More Complex Systems, F. Axel and J.-P. Gazeau, eds., Les Editions de Physique, Springer-Verlag, Berlin, 2000, pp. 145-166.
13. B. Praggastis, Numeration systems and Markov partitions from self similar tilings, Trans. Amer. Math. Soc. 351(8) (1999), 3315-3349.
14. C. Radin and M. Wolff, Space tilings and local isomorphism, Geom. Dedicata 42 (1992), 355-360.
15. R. M. Robinson, Undecidability and nonperiodicity for tilings of the plane, Invent. Math. 12 (1971), 177-209.
16. M. Schlottmann, Generalized model sets and dynamical systems, in Directions in Mathematical Quasicrystals, M. Baake and R. V. Moody, eds., CRM Monograph Series, Vol. 13, AMS, Providence, RI, 2000, pp. 143-159.
17. B. Solomyak, Dynamics of self-similar tilings, Ergodic Theory Dynamical Systems 17 (1997), 695-738.
18. B. Solomyak, Corrections to "Dynamics of self-similar tilings," Ergodic Theory Dynamical Systems 19 (1999), 1685.
19. A. Vince, Digit tiling of Euclidean space, in Directions in Mathematical Quasicrystals, M. Baake and R. V. Moody, eds., CRM Monograph Series, Vol. 13, AMS, Providence, RI, 2000, pp. 329-370.