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Motivated by recent work of George Andrews and Mircea Merca on the expansion of the quotient of the truncation of Euler's pentagonal number series by the complete series, we provide similar expansion results for averages involving…

A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems…

For a polynomial $P$ mapping the integers into the integers, define an averaging operator $A_{N} f(x):=\frac{1}{N}\sum_{k=1}^N f(x+P(k))$ acting on functions on the integers. We prove sufficient conditions for the $\ell^{p}$-improving…

In this paper we show that the ergodic averages of the action of any unimodular amenable group along certain F{\o}lner sequences can be dominated by the Ces\`aro means of a suitably constructed Markov operator, that is, the ergodic averages…

Recently, there has been an increasing interest on nonautonomous composition of perturbed hyperbolic systems: composing perturbations of a given hyperbolic map $F$ results in statistical behaviour close to that of $F$. We show this fact in…

We establish a generalization of Bourgain double recurrence theorem and ergodic Bourgain-Sarnak's theorem by proving that for any aperiodic $1$-bounded multiplicative function $\boldsymbol{\nu}$, for any map $T$ acting on a probability…

A universally L^1 good sequence n_k is constructed with n_{k+1}-n_k tending to infinity. For ergodic transformations non-conventional ergodic averages of L^1 functions computed by using this sequence converge to the integral of the…

In the present paper we consider a von Neumann algebra M with a faithful normal semi-finite trace $\t$, and $\{\alpha_ t\} $ a strongly continuous extension to $L^p(M,\t)$ of a semigroup of absolute contractions on $L^1 (M,\tau)$. By means…

Uniform asymptotic expansions are derived for the zeros of the reverse generalized Bessel polynomials of large degree $n$ and real parameter $a$. It is assumed that $-\Delta_{1} n+\frac{3}{2} \leq a \leq \Delta_{2} n$ for fixed arbitrary…

Given a smooth curve with nonzero curvature $\Sigma\subset \mathbb{R}^2$, let $E_{\Sigma}$ denote the associated Fourier extension operator. For both general compact curves and the parabola, we characterize the pairs $(p,q)\in [1,\infty]^2$…

Let $G$ be a countable abelian group. We study ergodic averages associated with configurations of the form $\{ag,bg,(a+b)g\}$ for some $a,b\in\mathbb{Z}$. Under some assumptions on $G$, we prove that the universal characteristic factor for…

Let $P: \F \times \F \to \F$ be a polynomial of bounded degree over a finite field $\F$ of large characteristic. In this paper we establish the following dichotomy: either $P$ is a moderate asymmetric expander in the sense that $|P(A,B)|…

Let B be a p-uniformly convex Banach space, with p >= 2. Let T be a linear operator on B, and let A_n x denote the ergodic average (1 / n) sum_{i< n} T^n x. We prove the following variational inequality in the case where T is power bounded…

We prove the $L^{2}$ convergence for the linear multiple ergodic averages of commuting transformations $T_{1}, ..., T_{l}$, assuming that each map $T_i$ and each pair $T_iT_j^{-1}$ is ergodic for $i\neq j$. The limiting behavior of such…

Using recent results on string on $AdS_{3}\times N^d$, where N is a d-dimensional compact manifold, we re-examine the derivation of the non trivial extension of the (1+2) dimensional-Poincar\'e algebra obtained by Rausch de Traubenberg and…

We investigate how spectral properties of a measure preserving system $(X,\mathcal{B},\mu,T)$ are reflected in the multiple ergodic averages arising from that system. For certain sequences $a:\mathbb{N}\to\mathbb{N}$ we provide natural…

We prove convergence in norm and pointwise almost everywhere on $L^p$, $p\in (1,\infty)$, for certain multi-parameter polynomial ergodic averages by establishing the corresponding multi-parameter maximal and oscillation inequalities. Our…

In this paper, we develop a method of evaluating general exponential sums with rational amplitude functions for multiple variables which complements works by T. Cochrane and Z. Zheng on the single variable case. As an application, for…

For $i = 0, 1, 2, \dots, k$, let $\mu_i$ be a Borel probability measure on $[0,1]$ which is equivalent to Lebesgue measure $\lambda$ and let $T_i:[0,1] \rightarrow [0,1]$ be $\mu_i$-preserving ergodic transformations. We say that…

Let $T$ be the Koopman operator of a measure preserving transformation $\theta$ of a probability space $(X,\Sigma,\mu)$. We study the convergence properties of the averages $M_nf:=\frac1n\sum_{k=0}^{n-1}T^kf$ when $f \in L^r(\mu)$, $0<r<1$.…