Page 1 Next

Displaying 1 – 20 of 123

Showing per page

A criterion of asymptotic stability for Markov-Feller e-chains on Polish spaces

Dawid Czapla (2012)

Annales Polonici Mathematici

Stettner [Bull. Polish Acad. Sci. Math. 42 (1994)] considered the asymptotic stability of Markov-Feller chains, provided the sequence of transition probabilities of the chain converges to an invariant probability measure in the weak sense and converges uniformly with respect to the initial state variable on compact sets. We extend those results to the setting of Polish spaces and relax the original assumptions. Finally, we present a class of Markov-Feller chains with a linear state space model which...

A ratio ergodic theorem for multiparameter non-singular actions

Michael Hochman (2010)

Journal of the European Mathematical Society

We prove a ratio ergodic theorem for non-singular free d and d actions, along balls in an arbitrary norm. Using a Chacon–Ornstein type lemma the proof is reduced to a statement about the amount of mass of a probability measure that can concentrate on (thickened) boundaries of balls in d . The proof relies on geometric properties of norms, including the Besicovitch covering lemma and the fact that boundaries of balls have lower dimension than the ambient space. We also show that for general group...

A spectral gap property for subgroups of finite covolume in Lie groups

Bachir Bekka, Yves Cornulier (2010)

Colloquium Mathematicae

Let G be a real Lie group and H a lattice or, more generally, a closed subgroup of finite covolume in G. We show that the unitary representation λ G / H of G on L²(G/H) has a spectral gap, that is, the restriction of λ G / H to the orthogonal complement of the constants in L²(G/H) does not have almost invariant vectors. This answers a question of G. Margulis. We give an application to the spectral geometry of locally symmetric Riemannian spaces of infinite volume.

Almost everywhere convergence and boundedness of Cesàro-α ergodic averages in Lp,q-spaces.

Francisco J. Martín Reyes, María Dolores Sarrión Gavilán (1999)

Publicacions Matemàtiques

Let (X, μ) be a σ-finite measure space and let τ be an ergodic invertible measure preserving transformation. We study the a.e. convergence of the Cesàro-α ergodic averages associated with τ and the boundedness of the corresponding maximal operator in the setting of Lp,q(wdμ) spaces.

Almost everywhere convergence of convolution powers on compact abelian groups

Jean-Pierre Conze, Michael Lin (2013)

Annales de l'I.H.P. Probabilités et statistiques

It is well-known that a probability measure μ on the circle 𝕋 satisfies μ n * f - f d m p 0 for every f L p , every (some) p [ 1 , ) , if and only if | μ ^ ( n ) | l t ; 1 for every non-zero n ( μ is strictly aperiodic). In this paper we study the a.e. convergence of μ n * f for every f L p whenever p g t ; 1 . We prove a necessary and sufficient condition, in terms of the Fourier–Stieltjes coefficients of μ , for the strong sweeping out property (existence of a Borel set B with lim sup μ n * 1 B = 1 a.e. and lim inf μ n * 1 B = 0 a.e.). The results are extended to general compact Abelian groups G with Haar...

Almost everywhere convergence of generalized ergodic transforms for invertible power-bounded operators in L p

Christophe Cuny (2011)

Colloquium Mathematicae

We show that some results of Gaposhkin about a.e. convergence of series associated to a unitary operator U acting on L²(X,Σ,μ) (μ is a σ-finite measure) may be extended to the case where U is an invertible power-bounded operator acting on L p ( X , Σ , μ ) , p > 1. The proofs make use of the spectral integration initiated by Berkson-Gillespie and, more specifically, of recent results of the author.

An exponential estimate for convolution powers

Roger Jones (1999)

Studia Mathematica

We establish an exponential estimate for the relationship between the ergodic maximal function and the maximal operator associated with convolution powers of a probability measure.

Asymptotic laws for geodesic homology on hyperbolic manifolds with cusps

Martine Babillot, Marc Peigné (2006)

Bulletin de la Société Mathématique de France

We consider a large class of non compact hyperbolic manifolds M = n / Γ with cusps and we prove that the winding process ( Y t ) generated by a closed 1 -form supported on a neighborhood of a cusp 𝒞 , satisfies a limit theorem, with an asymptotic stable law and a renormalising factor depending only on the rank of the cusp 𝒞 and the Poincaré exponent δ of Γ . No assumption on the value of δ is required and this theorem generalises previous results due to Y. Guivarc’h, Y. Le Jan, J. Franchi and N. Enriquez.

Axiomatic theory of divergent series and cohomological equations

Yu. I. Lyubich (2008)

Fundamenta Mathematicae

A general theory of summation of divergent series based on the Hardy-Kolmogorov axioms is developed. A class of functional series is investigated by means of ergodic theory. The results are formulated in terms of solvability of some cohomological equations, all solutions to which are nonmeasurable. In particular, this realizes a construction of a nonmeasurable function as first conjectured by Kolmogorov.

Banach principle in the space of τ-measurable operators

Michael Goldstein, Semyon Litvinov (2000)

Studia Mathematica

We establish a non-commutative analog of the classical Banach Principle on the almost everywhere convergence of sequences of measurable functions. The result is stated in terms of quasi-uniform (or almost uniform) convergence of sequences of measurable (with respect to a trace) operators affiliated with a semifinite von Neumann algebra. Then we discuss possible applications of this result.

Conjugacies between ergodic transformations and their inverses

Geoffrey Goodson (2000)

Colloquium Mathematicae

We study certain symmetries that arise when automorphisms S and T defined on a Lebesgue probability space (X, ℱ, μ) satisfy the equation S T = T - 1 S . In an earlier paper [6] it was shown that this puts certain constraints on the spectrum of T. Here we show that it also forces constraints on the spectrum of S 2 . In particular, S 2 has to have a multiplicity function which only takes even values on the orthogonal complement of the subspace f L 2 ( X , , μ ) : f ( T 2 x ) = f ( x ) . For S and T ergodic satisfying this equation further constraints arise,...

Currently displaying 1 – 20 of 123

Page 1 Next