A class of generalized Ornstein transformations with the weak mixing property
El Abdalaoui, El Houcein
Annales de l'I.H.P. Probabilités et statistiques, Tome 36 (2000), p. 775-786 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 2000-01-01
@article{AIHPB_2000__36_6_775_0,
     author = {El Abdalaoui, El Houcein},
     title = {A class of generalized Ornstein transformations with the weak mixing property},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {36},
     year = {2000},
     pages = {775-786},
     mrnumber = {1797393},
     zbl = {0969.28008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2000__36_6_775_0}
}

El Abdalaoui, El Houcein. A class of generalized Ornstein transformations with the weak mixing property. Annales de l'I.H.P. Probabilités et statistiques, Tome 36 (2000) pp. 775-786. http://gdmltest.u-ga.fr/item/AIHPB_2000__36_6_775_0/

[1] Bourgain J., On the spectral type of Ornstein's class one transformations, Israel J. Math. 84 (1993) 53-63. | MR 1244658 | Zbl 0787.28011

[2] Blum J.R., Cogburn R., On ergodic sequences of measures, Proc. Amer. Math. Soc. 51 (1975) 359-365. | MR 372529 | Zbl 0309.43001

[3] Choksi J.R., Nadkarni M.G., The group of eigenvalues of a rank one transformation, Canad. Math. Bull. 38 (1) (1995) 42-54. | MR 1319899 | Zbl 0833.28008

[4] El Abdalaoui E.H., A large class of Ornstein transformations with mixing property, Canad. Math. Bull., to appear. | MR 1754020 | Zbl 0967.37005

[5] El Abdalaoui E.H., La singularité mutuelle presque sûre du spectre des transformations d'Ornstein, Israel J. Math. 112 (1999) 135-156. | MR 1715002 | Zbl 0967.37004

[6] Friedman N.A., Introduction to Ergodic Theory, Van Nostrand - Reinhold, New York, 1970. | MR 435350 | Zbl 0212.40004

[7] Friedman N.A., Replication and stacking in ergodic theory, Amer. Math. Monthly 99 (1992) 31-34. | MR 1140275 | Zbl 0760.28012

[8] Kuipers L., Niederreiter H., Uniform Distribution of Sequences, Wiley-Interscience, New York, 1974. | MR 419394 | Zbl 0281.10001

[9] Nadkarni M.G., Spectral Theory of Dynamical Systems, Hindustan Book Agency, New Delhi, 1998; To appear in Europe under Birkhauser. | MR 1719722 | Zbl 1038.37502

[10] Nogueira A., Rudolph D., Topological weak-mixing of interval exchange maps, Ergodic Theory Dynamical Systems 17 (1997) 1183-1209. | MR 1477038 | Zbl 0958.37010

[11] Ornstein D.S., On the root problem in ergodic theory, in: Proc. Sixth Berkeley Symposium in Math. Statistics and Probability, University of California Press, 1971, pp. 347-356. | MR 399415 | Zbl 0262.28009

[12] Thouvenot J.-P., private communication.

[13] Veech W.A., A criterion for a process to be prime, Monatsh. Math. 94 (1982) 335-341. | MR 685378 | Zbl 0499.28016