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A Multiparameter, Zero Density Subsequence Ergodic Theorem

Published online by Cambridge University Press:  20 November 2018

Kurt D. Cogswell
Kurt D. Cogswell*
Affiliation:
Northwestern University Evanston, Illinois 60208 U.S.A.
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Abstract

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We generalize a result of L. Sucheston on obtaining multiparameter ergodic theorems from their single parameter versions. This result is then employed to prove a multiparameter, subsequence ergodic theorem for operator averages along special zero density subsequences.

Keywords

47A3528D99

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 1 , 01 March 1993 , pp. 33 - 37
Copyright
Copyright © Canadian Mathematical Society 1993

References

1. Akcoglu, M. A., A Pointwise Ergodic Theorem in Lp-Spaces, Canad. J. Math. 27(1975), 1075–1082.Google Scholar
2. Bourgain, J., On the Pointwise Ergodic Theorem for Arithmetic Sets, IHES publication, October, 1989.Google Scholar
3. Frangos, N. E. and Sucheston, L., On Multiparameter Ergodic and Martingale Theorems in Infinite Measure Spaces, Probab. Theor. Rel. Fields 71(1986), 477–490.Google Scholar
4. Ionescu-Tulcea, A., Ergodic Properties of I some trie s in Lp Spaces, 1 < p < ∞, Bull. A.M.S. 70(1964), 366–371.Google Scholar
5. Jones, R. L. and Olsen, J. H., Subsequence Ergodic Theorems for Operators, Israel J. Math., to appear.Google Scholar
6. Jones, R. L., Olsen, J. H. and Wierdl, M., Subsequence Ergodic Theorems for LP Contractions, Trans. A.M.S., to appear.Google Scholar
7. Kan, C.-H., Ergodic Properties of Lamperti Operators, Canad. J. Math. 30(1978), 1206–1214.Google Scholar
8. Olsen, J., Multi-Parameter Weighted Ergodic Theorems From Their Single Parameter Versions. In: Almost Everywhere Convergence, Academic Press, 1989, 297–303.Google Scholar
9. Sucheston, L., On One Parameter Proofs of Almost Sure Convergence of Multiparameter Processes, ZW 63(1983),43–49.Google Scholar
10. Wierdl, M., Pointwise Ergodic Theorem Along the Prime Numbers, Israel J. Math. 64(1988), 315–336.Google Scholar