The Ergodic Hilbert Transform for Admissible Processes
Canadian mathematical bulletin, Tome 49 (2006) no. 2, pp. 203-212

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2006-021-2
Mots-clés : 28D05, 37A99, Hilbert transform, admissible processes
Çömez, Doğan. The Ergodic Hilbert Transform for Admissible Processes. Canadian mathematical bulletin, Tome 49 (2006) no. 2, pp. 203-212. doi: 10.4153/CMB-2006-021-2
@article{10_4153_CMB_2006_021_2,
     author = {\c{C}\"omez, Do\u{g}an},
     title = {The {Ergodic} {Hilbert} {Transform} for {Admissible} {Processes}},
     journal = {Canadian mathematical bulletin},
     pages = {203--212},
     year = {2006},
     volume = {49},
     number = {2},
     doi = {10.4153/CMB-2006-021-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-021-2/}
}
TY  - JOUR
AU  - Çömez, Doğan
TI  - The Ergodic Hilbert Transform for Admissible Processes
JO  - Canadian mathematical bulletin
PY  - 2006
SP  - 203
EP  - 212
VL  - 49
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-021-2/
DO  - 10.4153/CMB-2006-021-2
ID  - 10_4153_CMB_2006_021_2
ER  - 
%0 Journal Article
%A Çömez, Doğan
%T The Ergodic Hilbert Transform for Admissible Processes
%J Canadian mathematical bulletin
%D 2006
%P 203-212
%V 49
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-021-2/
%R 10.4153/CMB-2006-021-2
%F 10_4153_CMB_2006_021_2

[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

Cité par Sources :