Related papers: An ergodic theorem for subadditive random function…

A semidomain is a subsemiring of an integral domain. We call a semidomain $S$ additively reduced if $0$ is the only invertible element of the monoid $(S, +)$, while we say that $S$ is additively Furstenberg if every non-invertible element…

The Birkhoff Ergodic Theorem concludes that time averages, i.e., Birkhoff averages, $\Sigma_{n=0}^{N-1} f(x_n)/N$ of a function $f$ along a length $N$ ergodic trajectory $(x_n)$ of a function $T$ converge to the space average $\int f d\mu$,…

For a connected semisimple real Lie group $G$ of non-compact type, Wallach introduced a class of $K$-types called small. We classify all small $K$-types for all simple Lie groups and prove except just one case that each elementary spherical…

Furstenberg, Katznelson and Weiss proved in the early 1980s that every measurable subset of the plane with positive density at infinity has the property that all sufficiently large real numbers are realised as the Euclidean distance between…

We investigate selfadjoint $C_0$-semigroups on Euclidean domains satisfying Gaussian upper bounds. Major examples are semigroups generated by second order uniformly elliptic operators with Kato potentials and magnetic fields. We study the…

Let $G$ be a connected linear algebraic group over a number field $K$, let $\Gamma$ be a finitely generated Zariski dense subgroup of $G(K)$ and let $Z\subseteq G(K)$ be a thin set, in the sense of Serre. We prove that, if…

Let $G$ be either a profinite or a connected compact group, and $\Gamma, \Lambda$ be finitely generated dense subgroups. Assuming that the left translation action of $\Gamma$ on $G$ is strongly ergodic, we prove that any cocycle for the…

In this paper, we discuss function theory on Teichm\"uller space through Thurston's theory, as well as the dynamics of subgroups of the mapping class group of a surface, with reference to Sullivan's theory on the ergodic actions of discrete…

Using functional calculi theory, we obtain several estimates for $\|\psi(A)g(A)\|$, where $\psi$ is a Bernstein function, $g$ is a bounded completely monotone function and $-A$ is the generator of a holomorphic $C_0$-semigroup on a Banach…

Let $G$ be a reductive group over a local field $F$ satisfying the assumptions of \cite{Deb1}, $G_{reg}\subset G$ the subset of regular elements. Let $T\subset G$ be a maximal torus. We write $T_{reg}=T\cap G_{reg}$. Let $dg ,dt$ be Haar…

Let $U$ be a horospherical subgroup of a noncompact simple Lie group $H$ and let $A$ be a maximal split torus in the normalizer of $U$. We define the expanding cone $A_U^+$ in $A$ with respect to $U$ and show that it can be explicitly…

For $\Cal A\subset L^1_{loc}(\Bbb J,X)$ let $\Cal M\Cal A$ consist of all $f\in L^1_{loc}$ with $ M_h f (\cdot):=\frac {1}{h}\int_{0}^{h}f(\cdot +s)\,ds \in \Cal A$ for all $h>0$. Here $X$ is a Banach space, $\Bbb J= (\alpha ,\infty),…

In cryptography and coding theory, it is important to study the pseudo-random sequences and the ergodic transformations. We already have the 1-Lipshitz ergodic theory over ${\Z}_2$ established by V. Anashin and others. In this paper we…

Let $\Omega\subset\R^N$ be an arbitrary open set and denote by $(e^{-t(-\Delta)_{\RR^N}^s})_{t\ge 0}$ (where $0<s<1$) the semigroup on $L^2(\RR^N)$ generated by the fractional Laplace operator. In the first part of the paper we show that if…

We consider a random walk $S_k$ with i.i.d. steps on a compact group equipped with a bi-invariant metric. We prove quantitative ergodic theorems for the sum $\sum_{k=1}^N f(S_k)$ with H\"older continuous test functions $f$, including the…

We study ergodic properties of compositions of holomorphic endomorphisms of the complex projective space chosen independently at random according to some probability distribution. Along the way, we construct positive closed currents which…

For $i=1,\ldots,k$, let $\mathbf{G}_i$ be a connected, simply connected, semisimple algebraic group over some local field $\kappa_i$ of characteristic zero. Let $G_i=\mathbf{G}_i(\kappa_i)$ be the $\kappa_i$-points of $\mathbf{G}_i$ and…

Let $G$ be a real semisimple Lie group with finite centre and without compact factors, $Q<G$ a parabolic subgroup and $X$ a homogeneous space of $G$ admitting an equivariant projection on the flag variety $G/Q$ with fibres given by copies…

An involution on a semigroup S (or any algebra with an underlying associative binary operation) is a function f:S->S that satisfies f(xy)=f(y)f(x) and f(f(x))=x for all x,y in S. The set I(S) of all such involutions on S generates a…

This article is the continuation of the work [DK] where we had proved maximal estimates $$\left\|\sup_{t > 0} |m(tA)f| \right\|_{L^p(\Omega,Y)} \leq C \|f\|_{L^p(\Omega,Y)}$$ for sectorial operators $A$ acting on $L^p(\Omega,Y)$ ($Y$ being…