Publication Cover
Dynamical Systems
An International Journal
Volume 27, 2012 - Issue 4
68
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

On the maximal spectral type of a class of rank one transformations

&
Pages 515-523 | Received 02 Nov 2011, Accepted 21 Aug 2012, Published online: 25 Sep 2012

References

  • Friedman , N . 1970 . “ Introduction to Ergodic Theory ” . In Van Nostrand Reinhold Mathematical Studies , Vol. 29 , New York : Van Nostrand Reinhold .
  • Ornstein. , DS . 1970 . On the root problem in ergodic theory , Proceedings of the 6th Berkeley Symposium on Mathematicval Statistics and Probability, University of California . Vol. 2, 1972, pp. 347–356
  • Katok , AB and Stepin , AM . 1967 . Approximations in ergodic theory . Usp. Mat. Nauk , 22 ( 5 (137) : 81 – 106 .
  • Chacon. , R . 1967 . A geometric construction of measure preserving transformations , 335 – 360 . Proceedings of the 5th Berkeley Symposium Mathematical Statistics and Probabability, University of California . Vol. 2, Part 2, 1965/66
  • Host , B . 1991 . Mixing of all orders and pairwise independent joinings of systems with singular spectrum . Isr. J. Math. , 76 ( 3 ) : 289 – 298 .
  • Bourgain , J . 1993 . On the spectral type of Ornstein's class one transformations . Isr. J. Math. , 84 ( 1–2 ) : 53 – 63 .
  • Klemes , I . 1996 . The spectral type of the staircase transformation . Tohoku Math. J. (2) , 48 ( 2 ) : 247 – 258 .
  • Klemes , I and Reinhold , K . 1997 . Rank one transformations with singular spectral type . Isr. J. Math. , 98 : 1 – 14 .
  • El Abdalaoui , EH . 2007 . A new class of rank-one transformations with singular spectrum . Ergodic Theory Dyn. Syst. , 27 ( 5 ) : 1541 – 1555 .
  • El Abdalaoui , EH , Parreau , F and Prikhodko , AA . 2006 . A new class of Ornstein transformations with singular spectrum . Ann. Inst. Henri Poincaré Probab. Statist. , 42 ( 6 ) : 671 – 681 .
  • Nadkarni , M . 1998 . Spectral Theory of Dynamical Systems , Birkhäuser, Basel : Birkhäuser Advanced Texts .
  • Choksi , J and Nadkarni , M . 1994 . The maximal spectral type of a rank one transformation . Can. Math. Bull. , 37 ( 1 ) : 29 – 36 .
  • Salem , R and Zygmund , A . 1947 . On lacunary trigonometric series . Proc. Natl. Acad. Sci. USA , 33 : 333 – 338 .
  • Salem , R and Zygmund , A . 1950 . La loi du logarithme iteré pour les séries trigonométriques lacunaires . Bull. Sci. Math., II. Ser. , 74 : 209 – 224 .
  • Aistleitner , C . 2010 . On the law of the iterated logarithm for the discrepancy of Lacunary sequences . Trans. Am. Math. Soc. , 362 ( 11 ) : 5967 – 5982 .
  • Aistleitner , C and Berkes , I . 2010 . On the central limit theorem for f(n k x) . Probab. Theory Relat. Fields , 146 ( 1–2 ) : 267 – 289 .
  • Erdös , P . 1962 . On trigonometric sums with gaps . Magyar Tud. Akad. Mat. Kutató Int. Közl , 7 : 37 – 42 .
  • Berkes , I . 1979 . A central limit theorem for trigonometric series with small gaps . Z. Wahrsch. Verw. Gebiete , 47 ( 2 ) : 157 – 161 .
  • Bobkov , SG and Götze , F . 2007 . Concentration inequalities and limit theorems for randomized sums . Probab. Theory Related Fields , 137 ( 1–2 ) : 49 – 81 .
  • Fukuyama , K . 2010 . “ A central limit theorem and a metric discrepancy result for sequences with bounded gaps ” . In Dependence in Probability, Analysis and Number Theory , Edited by: Berkes , I , Bradley , RC , Dehling , H , Peligrad , M and Tichy , R . 233 – 246 . Heber City , , UT : Kendrick Press .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.