Related papers: Hausdorff Measure for a Stable-Like Process over a…

We construct a family of non-PCF dendrites $K$ in a plane, such that in each of them all subarcs have the same Hausdorff dimension $s$, while the set of $s$-dimensional Hausdorff measures of subarcs connecting the given point and a…

We consider a minimal equicontinuous action of a finitely generated group $G$ on a Cantor set $X$ with invariant probability measure $\mu$, and stabilizers of points for such an action. We give sufficient conditions under which there exists…

We consider the class of stationary-increment harmonizable stable processes with infinite control measure, which most notably includes real harmonizable fractional stable motions. We give conditions for the integrability of the paths of…

Let K be a self-similar or self-affine set in R^d, let \mu be a self-similar or self-affine measure on it, and let G be the group of affine maps, similitudes, isometries or translations of R^d. Under various assumptions (such as separation…

We study continuity and discontinuity properties of some popular measure-dimension mappings under some topologies on the space of probability measures in this work. We give examples to show that no continuity can be guaranteed under general…

We introduce two families of infinite iterated function systems (IFSs) $\mathcal{F}(\mathbf{d}, T)$ and $\mathcal{G}(\mathbf{d}, T)$, parametrized by a sequence of positive real numbers $\mathbf{d}$ and a natural number $T$, and investigate…

Let $B$ be an $n\times n$ real expanding matrix and $\mathcal{D}$ be a finite subset of $\mathbb{R}^n$ with $0\in\mathcal{D}$. The self-affine set $K=K(B,\mathcal{D})$ is the unique compact set satisfying the set-valued equation…

Let $K\subset \mathbb{R}$ be a self-similar set generated by some iterated function system. In this paper we prove, under some assumptions, that $K$ can be identified with a subshift of finite type. With this identification, we can…

Let $B$ be a $d$-dimensional Gaussian process on $\mathbb{R}$, where the component are independents copies of a scalar Gaussian process $B_0$ on $\mathbb{R}_+$ with a given general variance function…

Let $T:X\to X$ be a linear power bounded operator on Banach space. Let $X_0$ is a subspace of vectors tending to zero under iterating of $T$. We prove that if $X_0$ is not equal to $X$ then there exists $\lambda$ in Sp(T) such that, for…

We characterize measure spaces such that the canonical map $L_\infty \to L_1^*$ is surjective. In case of $d$ dimensional Hausdorff measure of a complete separable metric space $X$ we give two equivalent conditions. One is in terms of the…

As a natural counterpart to Nakada's $\alpha$-continued fraction maps, we study a one-parameter family of continued fraction transformations with an indifferent fixed point. We prove that matching holds for Lebesgue almost every parameter…

We introduce the notion of tubular dimension, and give a formula for it. As an application we show that every invariant measure of a $C^{1+\gamma}$ diffeomorphism of a closed Riemannian manifold admits an asymptotic local product structure…

Generalizing a theorem of Ph. Dwinger, we describe the partially ordered set of all (up to equivalence) zero-dimensional locally compact Hausdorff extensions of a zero-dimensional Hausdorff space. Using this description, we find the…

There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions…

Let $\boldsymbol{B}_{[0,\infty)}$ be the semigroup which is defined in the Ahre paper \cite{Ahre=1981}. The semigroup $\boldsymbol{B}_{[0,\infty)}$ with the induced usual topology $\tau_u$ from $\mathbb{R}^2$, with the topology $\tau_L$…

We prove a Krieger like embedding theorem for asymptotically expansive systems with the small boundary property. We show that such a system $(X; T)$ embeds in the $K$-full shift with $h_{top}(T) < \log K $ and $\sharp Per_n(X; T) \leq…

We study the spectral properties of the Sturm Hamiltolian of eventually constant type, which includes the Fibonacci Hamiltonian. Let $s$ be the Hausdorff dimension of the spectrum. For $V>20$, we show that the restriction of the…

The main result of this paper is to show that if $\H$ is a normal subgroup of a Kleinian group $G$ such that $G/\H$ contains a coset which is represented by some loxodromic element, then the Hausdorff dimension of the transient limit set of…

In this paper we establish a direct connection between stable approximate unitary equivalence for $*$-homomorphisms and the topology of the KK-groups which avoids entirely C*-algebra extension theory and does not require nuclearity…