Related papers: Dimension estimates for invariant measures of cont…
We consider a general schema involving measure spaces, contractions and linear and continuous operators. Within the framework of this schema we use our sesquilinear uniform integral and introduce some integral operators on continuous vector…
Measures generated by Iterated Function Systems composed of uncountably many one--dimensional affine maps are studied. We present numerical techniques as well as rigorous results that establish whether these measures are absolutely or…
We introduce a pointwise variant of the Assouad dimension for measures on metric spaces, and study its properties in relation to the global Assouad dimension. We show that, in general, the value of the pointwise Assouad dimension differs…
We provide a rigorous study on dimensions of fractal interpolation function defined on a closed and bounded interval of $\mathbb{R}$ which is associated to a continuous function with respect to a base function, scaling functions and a…
We generalise Hochman's theorem on the dimension of self-similar measures to contracting on average measures and show that a weaker condition than exponential separation on all scales is sufficient. Our proof uses a technique we call the…
Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…
We study asymptotics for the intergal of irrationality measure functions.
We consider iterated function systems on the real line that consist of continuous, piecewise linear functions. We show that typically the natural dimension of these systems changes continuously with respect to the parameters that define the…
Geometric lower and upper estimates are obtained for invariant metrics on $\Bbb C$-convex domains containing no complex lines.
We prove weighted and vector-valued variational estimates for ergodic averages on $\mathbb{R}^d$. The weighted square function estimate relating ergodic averages to the dyadic martingale is obtained using an $\ell^r$ version of a reverse…
We consider the question of computing invariant measures from an abstract point of view. We work in a general framework (computable metric spaces, computable measures and functions) where this problem can be posed precisely. We consider…
We study certain multiple ergodic averages of an iterated functions system generated by two contractions on the unit interval. By using the dynamical coding ${0,1}^{\mathbb{N}}$ of the attractor, we compute the Hausdorff dimension of the…
We consider the dimension and measure of typical attractors of random iterated function systems (RIFSs). We define a RIFS to be a finite set of (deterministic) iterated function systems (IFSs) acting on the same metric space and, for a…
We study Whitney-type estimates for approximation of convex functions in the uniform norm on various convex multivariate domains while paying a particular attention to the dependence of the involved constants on the dimension and the…
In the paper, we study the generalized $q$-dimensions of measures supported by nonautonomous attractors, which are the generalization of classic Moran sets and attractors of iterated function systems. First, we estimate the generalized…
We investigate a linear operator associated with a functional equation that arises from studying some class of invariant measures under multidimensional transformations. By examining its iterates, we derive an explicit solution formula for…
We estimate the growth of the canonical integral of Hadamard-Weierstrass of measure of finite order on the complex plane by the type of counting function or average counting function of this measure
We discuss the properties of invariant measures corresponding to iterated function systems (IFSs) with place-dependent probabilities and compute their Renyi entropies, generalized dimensions, and multifractal spectra. It is shown that with…
Let $\nu$ be a Borel probability measure on a $d$-dimensional Euclidean space $\mathbb{R}^d$, $d\geq 1$, with a compact support, and let $(p_0, p_1, p_2, \ldots, p_N)$ be a probability vector with $p_j>0$ for $0\leq j\leq N$. Let $\{S_j:…
This note is concerned with lower tail estimates for product measures. Some improved deviation inequalities are obtained for functions satisfying some regularity and monotonicity assumptions. The arguments are based on semigroup…