Décomposition et classification des systèmes dynamiques
Des produits de Riesz comme mesures spectrales
Differentiation of Banach-space-valued additive processes
Dilations of Positive Operators: Construction and Ergodic Theory.
Dirichlet series and uniform ergodic theorems for linear operators in Banach spaces
We study the convergence properties of Dirichlet series for a bounded linear operator T in a Banach space X. For an increasing sequence of positive numbers and a sequence of functions analytic in neighborhoods of the spectrum σ(T), the Dirichlet series for is defined by D[f,μ;z](T) = ∑n=0∞ e-μnz fn(T), z∈ ℂ. Moreover, we introduce a family of summation methods called Dirichlet methods and study the ergodic properties of Dirichlet averages for T in the uniform operator topology.
Disjointness of the convolutionsfor Chacon's automorphism
The purpose of this paper is to show that if σ is the maximal spectral type of Chacon’s transformation, then for any d ≠ d’ we have . First, we establish the disjointness of convolutions of the maximal spectral type for the class of dynamical systems that satisfy a certain algebraic condition. Then we show that Chacon’s automorphism belongs to this class.
Domain characterizations of certain functions of power-bounded operators
We create a general framework for describing domains of functions of power-bounded operators given by power series with log-convex coefficients. This sheds new light on recent results of Assani, Derriennic, Lin and others. In particular, we resolve an open problem regarding the "one-sided ergodic Hilbert transform" formulated in a 2001 paper by Derriennic and Lin.
Dominated ergodic theorems in rearrangement invariant spaces
We study conditions under which Dominated Ergodic Theorems hold in rearrangement invariant spaces. Consequences for Orlicz and Lorentz spaces are given. In particular, our results generalize the classical theorems for the spaces and the classes .
Doubly stochastic operators on a finite-dimensional simplex.
Dynamical systems with multiplicative perturbations: the strong convergence of measures
We give sufficient conditions for the strong asymptotic stability of the distributions of dynamical systems with multiplicative perturbations. We apply our results to iterated function systems.