The multiplier-series of a Schottky group.
The one-sided ergodic Hilbert transform in Banach spaces
Let T be a power-bounded operator on a (real or complex) Banach space. We study the convergence of the one-sided ergodic Hilbert transform . We prove that weak and strong convergence are equivalent, and in a reflexive space also is equivalent to the convergence. We also show that (which converges on (I-T)X) is precisely the infinitesimal generator of the semigroup .
The Pascal adic transformation is loosely Bernoulli
The Poisson formula for groups with hyperbolic properties.
The Prime Orbit Theorem for Quasihyperbolic Toral Automorphisms.
The problem of -simple spectrum for ergodic group automorphisms
The quasi-sure ratio ergodic theorem
The rate of convergence of iterates of the Frobenius-Perron operator for piecewise monotonic transformations
The rearrangement inequality for the ergodic maximal function.
The return time theorem fails on infinite measure-preserving systems
The rotation number of some transformation related to billiards in an ellipse
The sequence entropy for Morse shifts and some counterexamples
The spectrum and commutant of a certain weighted translation operator.
The Speed of Convergence in Ergodic Theorem.
The Stein-Weiss theorem for the ergodic Hilbert transform
The Stein-Weiss theorem that the distribution function of the Hilbert transform of the characteristic function of E depends only on the measure of E is generalized for the ergodic Hilbert transform in the case of a one-parameter flow of measure-preserving transformations on a σ-finite measure space.
The topological centralizers of Toeplitz flows and their Z2-extensions.
The topological centralizers of Toeplitz flows satisfying a condition (Sh) and their Z2-extensions are described. Such Toeplitz flows are topologically coalescent. If {q0, q1, ...} is a set of all except at least one prime numbers and I0, I1, ... are positive integers then the direct sum ⊕i=0∞ Zqi|i ⊕ Z can be the topological centralizer of a Toeplitz flow.
The variational principle
The vector individual weighted ergodic theorem for bounded Besicovich sequences.
The σ-ideal of closed smooth sets does not have the covering property
We prove that the σ-ideal I(E) (of closed smooth sets with respect to a non-smooth Borel equivalence relation E) does not have the covering property. In fact, the same holds for any σ-ideal containing the closed transversals with respect to an equivalence relation generated by a countable group of homeomorphisms. As a consequence we show that I(E) does not have a Borel basis.
Théorème ergodique ponctuel pour les suites uniformes