Dworkin’s argument revisited: Point processes, dynamics, diffraction, and correlations
Tài liệu tham khảo
M. Baake, M. Birkner, R.V. Moody, Diffraction of stochastic point sets: exactly solvable models, preprint, 2007
Baake, 2004, Dynamical systems on translation bounded measures: Pure point dynamical and diffraction spectra, Ergodic Theory & Dynam. Systems, 24, 1867, 10.1017/S0143385704000318
Baake, 2004, Weighted Dirac combs with pure point diffraction, J. Reine Angew. Math. (Crelle), 573, 61
Berg, 1975
Cohn, 1997
Daley, 2002, vol. 1
Dekking, 1978, The spectrum of dynamical systems arising from substitutions of constant length, Z. Wahrscheinlichkeitstheorie verw. Geb., 41, 221, 10.1007/BF00534241
Xinghua Deng, How finite correlations determine uniformly discrete point processes: Examples (in preparation)
Dieudonné, 1970, Vol. 2
Dworkin, 1993, Spectral theory and X-ray diffraction, J. Math. Phys., 34, 2965, 10.1063/1.530108
Gouéré, 2005, Quasicrystals and almost periodicity, Comm. Math. Phys., 255, 651, 10.1007/s00220-004-1271-8
Hof, 1995, On diffraction by aperiodic structures, Comm. Math. Phys., 169, 25, 10.1007/BF02101595
Hof, 1997, Diffraction by aperiodic structures, vol. 489, 239
Hof, 1995, Diffraction by aperiodic structures at high temperatures, J. Phys. A: Math. Gen., 28, 57, 10.1088/0305-4470/28/1/012
Kakutani, 1967, Ergodic theory of shift transformations, 405
Kakutani, 1972, Vol. 2, 319
Karr, 1991
Keane, 1968, Generalized Morse sequences, Z. Wahrscheinlichkeitstheorie verw. Geb., 10, 335, 10.1007/BF00531855
Lee, 2002, Pure point dynamical and diffraction spectra, Ann. H. Poincaré, 3, 1003, 10.1007/s00023-002-8646-1
D. Lenz, On a conjecture by Bombieri and Taylor, preprint, 2007
D. Lenz, R.V. Moody, Extinctions and correlations for uniformly discrete point processes with pure point dynamical spectra (in preparation)
Martin, 1973, Minimal flows arising from substitutions of non-constant length, Math. Syst. Th., 7, 73, 10.1007/BF01824809
Moody, 1997, Model sets and their duals, vol 489, 239
Priebe–Frank, 2003, Substitution sequences in Zd with a nonsimple Lebesgue component in the spectrum, Ergodie Theory & Dynam. Systems, 23, 519
Queffélec, 1987, vol. 1294
Radin, 1992, Geom. Dedicata, 42, 355, 10.1007/BF02414073
Rudin, 1962
Schlottmann, 2000, Generalized model sets and dynamical systems, vol. 13, 143
Schwartz, 1966
van Enter, 1992, How should one define a (weak) crystal?, J. Stat. Phys., 66, 10.1007/BF01055722