Appendix on return-time sequences

Jean Bourgain; Harry Furstenberg; Yitzhak Katznelson; Donald S. Ornstein

Publications Mathématiques de l'IHÉS (1989)

  • Volume: 69, page 42-45
  • ISSN: 0073-8301

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Bourgain, Jean, et al. "Appendix on return-time sequences." Publications Mathématiques de l'IHÉS 69 (1989): 42-45. <http://eudml.org/doc/104054>.

@article{Bourgain1989,
author = {Bourgain, Jean, Furstenberg, Harry, Katznelson, Yitzhak, Ornstein, Donald S.},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {measure-preserving automorphism; polynomial with integer coefficients; pointwise ergodic theorem; Birkhoff's ergodic theorem; return times; ergodic system; inequality on martingales},
language = {eng},
pages = {42-45},
publisher = {Institut des Hautes Études Scientifiques},
title = {Appendix on return-time sequences},
url = {http://eudml.org/doc/104054},
volume = {69},
year = {1989},
}

TY - JOUR
AU - Bourgain, Jean
AU - Furstenberg, Harry
AU - Katznelson, Yitzhak
AU - Ornstein, Donald S.
TI - Appendix on return-time sequences
JO - Publications Mathématiques de l'IHÉS
PY - 1989
PB - Institut des Hautes Études Scientifiques
VL - 69
SP - 42
EP - 45
LA - eng
KW - measure-preserving automorphism; polynomial with integer coefficients; pointwise ergodic theorem; Birkhoff's ergodic theorem; return times; ergodic system; inequality on martingales
UR - http://eudml.org/doc/104054
ER -

References

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  1. [B1] J. BOURGAIN, On the maximal ergodic theorem for certain subsets of the integers, Israel J. Math., 61 (1) (1988), 39-72. Zbl0642.28010MR89f:28037a
  2. [B2] J. BOURGAIN, On the pointwise ergodic theorem on Lp for arithmetic sets, ibid., 73-84. Zbl0642.28011MR89f:28037b
  3. [B3] J. BOURGAIN, An approach to pointwise ergodic theorems, Springer LNM, 1317 (1988), 204-223. Zbl0662.47006MR90b:28016
  4. [B4] J. BOURGAIN, Return time sequences of dynamical systems, preprint IHES, 3/1988. 
  5. [B5] J. BOURGAIN, Almost sure convergence and bounded entropy, Israel J. Math., 63 (1) (1988), 79-97. Zbl0677.60042MR89k:60052
  6. [B6] J. BOURGAIN, Temps de retour pour les systèmes dynamiques, CRASc Paris, Ser I, 306 (1988), 483-485. Zbl0655.58022MR89e:28025
  7. [Fu] H. FURSTENBERG, Recurrence in ergodic theory and combinatorial number theory, Princeton UP, 1981. Zbl0459.28023MR82j:28010
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  10. [Lé] D. LÉPINGLE, La variation d'ordre p des semi-martingales, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 36 (1976), 295-316. Zbl0325.60047MR54 #8849
  11. [Ma] J. M. MARSTRAND, On Khinchine's conjecture about strong uniform distribution, Proc. London Math. Soc., 21 (1970), 540-556. Zbl0208.31402MR45 #185
  12. [Nev] J. NEVEU, Martingales à temps discret, Masson, 1972. MR53 #6728
  13. [Ra] D. A. RAIKOV, On some arithmetical properties of summable functions, Mat. Sb., 1 (43) (1936), 377-384. Zbl0014.39701
  14. [Ri] F. RIESZ, Sur la théorie ergodique, Comment. Math. Helv., 17 (1945), 221-239. Zbl0063.06500MR7,255b
  15. [S] R. SALEM, Collected works, Hermann, Paris, 1967. 
  16. [St] E. STEIN, On limits of sequences of operators, Ann. Math., 74 (1961), 140-170. Zbl0103.08903MR23 #A2695
  17. [Vaug] R. C. VAUGHAN, The Hardy-Littlewood method, Cambridge Tracts, 70 (1981). Zbl0455.10034MR84b:10002
  18. [Vin] I. M. VINOGRADOV, The method of trigonometrical sums in the theory of numbers, Interscience N. Y., 1954. Zbl0055.27504
  19. [W] B. WEISS, Private communications. 
  20. [W1] M. WIERDL, Pointwise ergodic theorem along the prime numbers, Israel J. Math., 64 (1988), 315-336. Zbl0695.28007MR90f:11062

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