Dense Dirac combs in Euclidean space with pure point diffraction

Journal of Mathematical Physics

Volumn 44, Issue 10, 2003, Pages 4436-4449

  Richard, Christoph ^a  

^a UNIVERSITY OF GREIFSWALD   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0142073347     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1609032     Document Type: Article

References (26)

1. Baake, M. and Höffe, M., "Diffraction of random tilings: Some rigorous results," J. Stat. Phys. 99, 219-261 (2000); math-ph/9904005.
2. Baake, M. and Moody, R.V., "Diffractive point sets with entropy," J. Phys. A 31, 9023-9039 (1998); math-ph/9809002.
3. Baake, M. and Moody, R.V., "Self-similar measures for quasicrystals," in Directions in Mathematical Quasicrystals, edited by M. Baake and R.V. Moody, CRM Monograph Series, Vol. 13 (AMS, Providence, RI, 2000), pp. 1-42; math.MG/0008063.
4. Baake, M. and Moody, R.V., "Weighted Dirac combs with pure point diffraction," math.MG/0203030 (2002).
5. Baake, M., Moody, R.V., and Pleasants, P.A.B., "Diffraction from visible lattice points and kth power free integers," Discrete Math. 221, 3-42 (2000); math.MG/9906132.
6. Baake, M., Moody, R.V., Richard, C., and Sing, B., "Which distributions of matter diffract? - Some answers," in Quasicrystals: Structure and Physical Properties, edited by H.-R. Trebin (Wiley-VCH, Berlin, 2003), pp. 188-207; math-ph/0301019.
7. Bernuau, G. and Duneau, M., "Fourier analysis of deformed model sets," in Directions in Mathematical Quasicrystals, edited by M. Baake and R.V. Moody, CRM Monograph Series, Vol. 13 (AMS, Providence, RI, 2000), pp. 43-60.
8. Bombieri, E. and Taylor, J.E., "Which distributions of matter diffract? An initial investigation," J. Phys. Colloq. 47, 19-28 (1986).
9. Córdoba, A., "Dirac combs," Lett. Math. Phys. 17, 191-196 (1989).
10. Dworkin, S., "Spectral theory and x-ray diffraction," J. Math. Phys. 34, 2965-2967 (1993).
11. Gil de Lamadrid, J. and Argabright, L.N., "Almost periodic measures," Memoirs of the AMS, Vol. 428 (AMS, Providence, RI, 1990).
12. Henley, C.L., "Random tiling models," in Quasicrystals: The State of the Art, 2nd ed. edited by D.P. DiVincenzo and P.J. Steinhardt, Series on Directions in Condensed Matter Physics, Vol. 16 (World Scientific, Singapore, 1999), pp. 459-560.
13. Hof, A., "On diffraction by aperiodic structures," Commun. Math. Phys. 169, 25-43 (1995).
14. Hof, A., "Uniform distribution and the projection method," in Quasicrystals and Discrete Geometry, edited by J. Patera, Fields Institute Monographs, Vol. 10 (AMS, Providence, RI, 1998), pp. 201-206.
15. Höffe, M., "Diffraktionstheorie stochastischer Parkettierungen," Dissertation, Universität Tübingen, Shaker, Aachen, 2001.
16. Höffe, M. and Baake, M., "Surprises in diffuse scattering," Z. Kristallogr. 215, 441-444 (2000); math-ph/0004022.
17. Kuipers, L. and Niederreiter, H., Uniform Distribution of Sequences (Wiley, New York, 1974).
18. Külske, C., "Universal bounds on the selfaveraging of random diffraction measures," math-ph/0109005 (2001).
19. Lagarias, J.C., "Mathematical quasicrystals and the problem of diffraction," in Directions in Mathematical Quasicrystals, edited by M. Baake and R.V. Moody, CRM Monograph Series, Vol. 13 (AMS, Providence, RI, 2000), pp. 61-93.
20. Lenz, D. (private communication, 2002).
21. Moody, R.V., "Meyer sets and their duals," in The Mathematics of Long-Range Aperiodic Order, edited by R.V. Moody, NATO ASI Series C 489 (Kluwer, Dordrecht, 1997), pp. 403-441.
22. Reed, M. and Simon, B., Methods of Modern Mathematical Physics. I: Functional Analysis, 2nd ed. (Academic, San Diego, CA, 1980).
23. Richard, C., "An alternative view on quasicrystalline random tilings," J. Phys. A 32, 8823-8829 (1999); cond-mat/9907262.
24. Richard, C., Höffe, M., Hermisson, J., and Baake, M., "Random tilings: Concepts and examples," J. Phys. A 31, 6385-6408 (1998); cond-mat/9712267.
25. Schlottmann, M., "Cut-and-project sets in locally compact Abelian groups," in Quasicrystals and Discrete Geometry, edited by J. Patera, Fields Institute Monographs, Vol. 10 (AMS, Providence, RI, 1998), pp. 247-264.
26. Schlottmann, M., "Generalized model sets and dynamical systems," in Directions in Mathematical Quasicrystals, edited by M. Baake and R.V. Moody, CRM Monograph Series, Vol. 13 (AMS, Providence, RI, 2000), pp. 143-159.