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The Ergodic Hilbert Transform for Admissible Processes

Published online by Cambridge University Press:  20 November 2018

Doğan Çömez
Doğan Çömez*
Affiliation:
Department of Mathematics, North Dakota State University, Fargo, ND 58105-5075, U.S.A e-mail: Dogan.Comez@ndsu.nodak.edu
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Abstract

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It is shown that the ergodic Hilbert transform exists for a class of bounded symmetric admissible processes relative to invertible measure preserving transformations. This generalizes the well-known result on the existence of the ergodic Hilbert transform.

Keywords

28D0537A99Hilbert transformadmissible processes
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 49 , Issue 2 , 01 June 2006 , pp. 203 - 212
Copyright
Copyright © Canadian Mathematical Society 2006

References

[AS] Akcoglu, M. A. and Sucheston, L., A ratio ergodic theorem for superadditive processes. Z. Wahrsch. Verw. Gebiete 44(1978), no. 4, 269–278.Google Scholar
[C] Cotlar, M., A unified theory of Hilbert transforms and ergodic theorems. Rev. Mat. Cuyana 1(1955), 105–167.Google Scholar
[CaP] Campell, J. and Petersen, K., The spectral measure and Hilbert transform of a measure-preserving transformation. Trans. Am. Math. Soc. 313(1989), 121–129.Google Scholar
[CoL] Cohen, G. and Lin, M., Laws of large numbers with rates and the one-sided ergodic Hilbert transform. Illinois J. Math. 47(2003), 997–1031.Google Scholar
[DL] Derriennic, Y. and Lin, M., Fractional Poisson equations and ergodic theorems for fractional coboundaries. Israel J. Math. 123(2001), 93–130.Google Scholar
[K] Kingman, J. F. C., The ergodic theory of subadditive stochastic processes. J. Roy. Statist. Soc. Ser. B 30(1968), 499–510.Google Scholar
[P1] Petersen, K., Another proof of the existence of the ergodic Hilbert transform. Proc. Am. Math. Soc. 88(1983), no. 1, 39–43.Google Scholar
[P2] Petersen, K., Ergodic Theory. Cambridge Studies in Advanced Mathematics 2, Cambridge University Press, Cambridge, 1983.Google Scholar