Absolutely continuous dynamics and real coboundary cocycles in L p -spaces, 0 < p < ∞

Ana Alonso; Jialin Hong; Rafael Obaya

Studia Mathematica (2000)

  • Volume: 138, Issue: 2, page 121-134
  • ISSN: 0039-3223

Abstract

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Conditions for the existence of measurable and integrable solutions of the cohomology equation on a measure space are deduced. They follow from the study of the ergodic structure corresponding to some families of bidimensional linear difference equations. Results valid for the non-measure-preserving case are also obtained

How to cite

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Alonso, Ana, Hong, Jialin, and Obaya, Rafael. "Absolutely continuous dynamics and real coboundary cocycles in $L^p$-spaces, 0 < p < ∞." Studia Mathematica 138.2 (2000): 121-134. <http://eudml.org/doc/216694>.

@article{Alonso2000,
abstract = {Conditions for the existence of measurable and integrable solutions of the cohomology equation on a measure space are deduced. They follow from the study of the ergodic structure corresponding to some families of bidimensional linear difference equations. Results valid for the non-measure-preserving case are also obtained},
author = {Alonso, Ana, Hong, Jialin, Obaya, Rafael},
journal = {Studia Mathematica},
keywords = {integrable cocycles},
language = {eng},
number = {2},
pages = {121-134},
title = {Absolutely continuous dynamics and real coboundary cocycles in $L^p$-spaces, 0 < p < ∞},
url = {http://eudml.org/doc/216694},
volume = {138},
year = {2000},
}

TY - JOUR
AU - Alonso, Ana
AU - Hong, Jialin
AU - Obaya, Rafael
TI - Absolutely continuous dynamics and real coboundary cocycles in $L^p$-spaces, 0 < p < ∞
JO - Studia Mathematica
PY - 2000
VL - 138
IS - 2
SP - 121
EP - 134
AB - Conditions for the existence of measurable and integrable solutions of the cohomology equation on a measure space are deduced. They follow from the study of the ergodic structure corresponding to some families of bidimensional linear difference equations. Results valid for the non-measure-preserving case are also obtained
LA - eng
KW - integrable cocycles
UR - http://eudml.org/doc/216694
ER -

References

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  10. [10] M. Lin and R. Sine, Ergodic theory and the functional equation (I-T)x= y , J. Operator Theory 10, 153-166 (1983). Zbl0553.47006
  11. [11] F. J. Martín-Reyes and A. de la Torre, On the pointwise ergodic theorem, Studia Math. 108, 1-4 (1994). Zbl0861.28011
  12. [12] S. Novo and R. Obaya, An ergodic classification of bidimensional linear systems, J. Dynam. Differential Equations 8, 373-406 (1996). Zbl0869.28009
  13. [13] S. Novo and R. Obaya, An ergodic and topological approach to almost periodic bidimensional linear systems, in: Contemp. Math. 215, Amer. Math. Soc., 1998, 299-323. Zbl0896.58041
  14. [14] R. Sato, Pointwise ergodic theorems in Lorentz spaces L(p,q) for null preserving transformations, Studia Math. 114, 227-236 (1995). Zbl0835.47006

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