A new class of Ornstein transformations with singular spectrum

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1. [1] T.R. Adams, On Smorodinsky conjecture, Proc. Amer. Math. Soc.126 (3) (1998) 739-744. Zbl0906.28006MR1443143
2. [2] T.R. Adams, N.A. Friedman, Staircase mixing, Ergodic Theory Dynam. Systems, in press. 
3. [3] A. Bonami, Ensembles $\Lambda \left(p\right)$ dans le dual de $D^{\infty }$, Ann. Inst. Fourier (Grenoble)15 (1968) 293-304. Zbl0175.44801
4. [4] J. Bourgain, On the spectral type of Ornstein class one transformations, Israel J. Math.84 (1993) 53-63. Zbl0787.28011MR1244658
5. [5] J.R. Choksi, M.G. Nadkarni, The maximal spectral type of rank one transformation, Canad. Math. Pull.37 (1) (1994) 29-36. Zbl0793.28013MR1261554
6. [6] D. Creutz, C.E. Silva, Mixing on a class of rank one transformations, Ergodic Theory Dynam. Systems24 (2) (2004) 407-440. Zbl1066.37003MR2054050
7. [7] R.M. Dudley, Real Analysis and Probability, Wadsworth & Brooks/Cole Math. Ser., Wadsworth & Brooks/Cole, Pacific Grove, CA, 1989. Zbl0686.60001MR982264
8. [8] E.H. El Abdalaoui, La singularité mutuelle presque sûre du spectre des transformations d'Ornstein, Israel J. Math.112 (1999) 135-155. Zbl0967.37004MR1715002
9. [9] E.H. El Abdalaoui, On the spectrum of the powers of Ornstein transformations, Special issue on Ergodic theory and harmonic analysis, Shankyā Ser. A62 (3) (2000) 291-306. Zbl0985.37003MR1803457
10. [10] N. Friedman, Replication and stacking in ergodic theory, Amer. Math. Monthly99 (1992) 31-34. Zbl0760.28012MR1140275
11. [11] N.A. Friedman, Introduction to Ergodic Theory, Van Nostrand Reinhold, New York, 1970. Zbl0212.40004MR435350
12. [12] I. Klemes, The spectral type of staircase transformations, Tohoku Math. J.48 (1994) 247-258. Zbl0853.28008MR1387818
13. [13] I. Klemes, K. Reinhold, Rank one transformations with singular spectre type, Israel J. Math.98 (1997) 1-14. Zbl0884.28011MR1459845
14. [14] M.G. Nadkarni, Spectral Theory of Dynamical Systems, Birkhäuser Advanced Texts: Basler Lehrbücher, Birkhäuser, Basel, 1998. Zbl0921.28009MR1719722
15. [15] D.S. Ornstein, 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. Zbl0262.28009MR399415
16. [16] W. Parry, Topics in Ergodic Theory, Cambridge University Press, 1981. Zbl0449.28016MR614142
17. [17] A.A. Prikhod'ko, Stochastic constructions of flows of rank 1, Sb. Math.192 (11–12) (2001) 1799-1828. Zbl1017.37002MR1885913
18. [18] D. Rudolph, An example of a measure-preserving map with minimal self-joining and applications, J. Anal. Math.35 (1979) 97-122. Zbl0446.28018MR555301