Related papers: Dimension of the harmonic measure of non-homogeneo…
In this paper, we give the Assouad dimension formula and the upper bound of the lower dimension for homogeneous Moran sets under the condition $\sup_{k\ge 1}\{n_{k}\}<+\infty$. We also give the Assouad spectrum and the lower spectrum…
By using a similar pattern of arguments, we show that in three categories the collection of isomorphisms forms a residual subset of the space of morphisms. We first consider surjective continuous mappings on Cantor spaces. Next, we look at…
In this paper, we study the harmonic analysis of Bernoulli measures. We show a variety of orthonormal Fourier bases for the L^2 Hilbert spaces corresponding to certain Bernoulli measures, making use of contractive transfer operators. 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
Let $T : \Lambda \to \Lambda$ be an expanding map on a Cantor set. For each suitably normalized H\"older continuous potential, we construct a spectral triple from which one may recover the associated Gibbs measure as a noncommutative…
The formulation of a new analysis on a zero measure Cantor set $C (\subset I=[0,1])$ is presented. A non-archimedean absolute value is introduced in $C$ exploiting the concept of {\em relative} infinitesimals and a scale invariant…
We prove variations of Carath\'eodory's, Helly's and Tverberg's theorems where the sets involved are measured according to continuous functions such as the volume or diameter. Among our results, we present continuous quantitative versions…
The article is devoted to the investigation of properties of quasi-invariant measures with values in non-Archimedean fields such as: convolutions of measures and functions; continuity of functions of measures; non-associative noncommutative…
We give a complete characterization of the size of Borel sets that are mid-point convex but not (essentially) convex, in terms of their Hausdorff dimensions and Hausdorff measures.
Let $f: M\rightarrow M$ be a continuous map on a compact metric space $M$ equipped with a fixed metric $d$, and let $\tau$ be the topology on $M$ induced by $d$. First, we will establish some fundamental properties of the mean Hausdorff…
Let $\{S_i\}_{i=1}^\ell$ be an iterated function system (IFS) on $\R^d$ with attractor $K$. Let $(\Sigma,\sigma)$ denote the one-sided full shift over the alphabet $\{1,..., \ell\}$. We define the projection entropy function $h_\pi$ on the…
We recall the definition of the $\epsilon$-distortion complexity of a set defined in \cite{bcc} and the results obtained in this paper for Cantor sets of the interval defined by iterated function systems. We state an analogous definition…
We show that in finite dimension a quantum measurement with continuous set of outcomes is always equivalent to a continuous random choice of measurements with only finite outcomes.
This note contains the complete mathematical proof of the main Theorem of the paper "How continuous measurements in finite dimension are actually discrete" (quant-ph/0702068), thus showing that in finite dimension any measurement with…
Considering the conformal anomaly in an effective action, the critical dimension of string theory can be decided in the harmonic gauge, in which it had been reported before to be indefinite. In this gauge, there is no anomaly for the ghost…
In this paper convergence theorems for sequences of scalar, vector and multivalued Pettis integrable functions on a topological measure space are proved for varying measures vaguely convergent.
In this work we determine and discuss the entropic uncertainty measures of Shannon type for all the discrete stationary states of the multidimensional harmonic systems directly in terms of the states' hyperquantum numbers, the…
It is proved that harmonic functions are characterized by harmonicity of their spherical means, for which purpose the iterated spherical means are used. The similar characterization of solutions to the modified Helmholtz equation…
In this note, we describe the Hermitian metrics that leave the total Monge-Ampere volume invariant. In particular, we give several characterizations of the Hermitian metrics which satisfy the comparison principle for the complex…
We analyze the boundaries of multiply connected Fatou components of transcendental maps by means of universal covering maps and associated inner functions. A unified approach is presented, which includes invariant Fatou components (of any…