Advertisement

Mathematische Annalen

, Volume 293, Issue 1, pp 399–426 | Cite as

Almost everywhere convergence of weighted averages

  • Alexandra Bellow
  • Roger L. Jones
  • Joseph Rosenblatt
Article

Keywords

Weighted Average 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Akcoglu, M., del Junco, A.: Convergence of averages of point transformations. Proc. Am. Math. Soc.49, 265–266 (1975)Google Scholar
  2. 2.
    Bellow, A., Losert, V.: The weighted pointwise ergodic theorem and the individual ergodic theorem along subsequences. Trans. Am. Math. Soc.288, 307–345 (1985)Google Scholar
  3. 3.
    Bellow, A., Jones, R., Rosenblatt, J.: Convergence for moving averages. Ergodic Theory Dyn. Syst.10, 43–62 (1990)Google Scholar
  4. 4.
    Bourgain, J.: On the maximal ergodic theorem for certain subsets of the integers. Isr. J. Math.61, 39–72 (1988)Google Scholar
  5. 5.
    Calderón, A.P.: Ergodic theory and translation-invariant operators. Proc. Natl. Acad. Sci. USA59, 349–353 (1968)Google Scholar
  6. 6.
    Déniel, Y.: On a.s. Cesàro-α convergence for stationary or orthogonal random variables. J. Theor. Probab.2, 475–485 (1989)Google Scholar
  7. 7.
    Duoandikoetxea, J., Rubio de Francia, J.: Maximal and singular integral operators via Fourier transform estimates. Invent. Math.84, 541–561 (1986)Google Scholar
  8. 8.
    Derriennic, Y.: Personal communicationGoogle Scholar
  9. 9.
    Emerson, W.R.: The pointwise ergodic theorem for amenable groups. Am. J. Math.96, 472–487 (1974)Google Scholar
  10. 10.
    Foguel, S.R.: On iterates of convolutions. Proc. Am. Math. Soc.47, 368–370 (1975)Google Scholar
  11. 11.
    Foguel, S.R.: Iterates of a convolution on a non-abelian group. Ann. Inst. Henri Poincaré11, 199–202 (1975)Google Scholar
  12. 12.
    Huang, Y.: Random sets for the pointwise ergodic theorem. Ph.d. Thesis, Northwestern University: 1989Google Scholar
  13. 13.
    Kahane, J.-P.: Some random series of functions, 2nd ed. Cambridge: Cambridge University Press 1985Google Scholar
  14. 14.
    Pier, J.-P.: Amenable locally compact groups. New York: John Wiley and Sons 1984Google Scholar
  15. 15.
    Petrov, V.V.: Sums of independent random variables. (Ergeb. Math., Grenzgeb., vol. 82) Berlin Heidelberg New York: Springer 1975Google Scholar
  16. 16.
    Rosenblatt, J.: Ergodic and mixing random walks on locally compact groups. Math. Ann.257, 31–42 (1981)Google Scholar
  17. 17.
    Rosenblatt, J.: Ergodic group actions. Arch. Math.47, 263–269 (1986)Google Scholar
  18. 18.
    Stein E.M.: On the maximal ergodic theorem. Proc. Natl. Acad. Sci. USA47, 1894–1897 (1961)Google Scholar
  19. 19.
    Tempelman, A.A.: Ergodic theorems for general dynamical systems. Sov. Math. Dokl.8, 1213–1216 (1967)Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Alexandra Bellow
    • 1
  • Roger L. Jones
    • 2
  • Joseph Rosenblatt
    • 3
  1. 1.Mathematics DepartmentNorthwestern UniversityEvanstonUSA
  2. 2.Mathematics Department DePaul UniversityChicagoUSA
  3. 3.Mathematics DepartmentOhio State UniversityColumbusUSA

Personalised recommendations