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Ergodic theory for the one-dimensional Jacobi operator

Carmen Núñez; Rafael Obaya — 1996

Studia Mathematica

We determine the number and properties of the invariant measures under the projective flow defined by a family of one-dimensional Jacobi operators. We calculate the derivative of the Floquet coefficient on the absolutely continuous spectrum and deduce the existence of the non-tangential limit of Weyl m-functions in the $L^{1}$ -topology.

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

Ana Alonso; Jialin Hong; Rafael Obaya — 2000

Studia Mathematica

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

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Ergodic theory for the one-dimensional Jacobi operator

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

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