Related papers: On the projections of the multifractal packing dim…
The aim of this paper is to study the behavior of the multifractal Hewitt-Stromberg dimension functions under projections in Euclidean space. As an application, we study the multifractal analysis of the projections of a measure. In…
The aim of this article is to study the behaviour of the relative multifractal spectrum under projections. First of all, we depict a relationship between the mutual multifractal spectra of a couple of measures $(\mu, \nu)$ and its…
In this paper, we study the multifractal Hausdorff and packing dimensions of Borel probability measures and study their behaviors under orthogonal projections. In particular, we try through these results to improve the main result of M. Dai…
We study the packing dimension of Borel measures under orthogonal projections. We give a necessary and sufficient condition such that typical projections of Borel probability measures have full packing dimension and derive general lower…
We prove preservation of $L^q$ dimensions (for $1<q\le 2$) under all orthogonal projections for a class of random measures on the plane, which includes (deterministic) homogeneous self-similar measures and a well-known family of measures…
We determine the $1$-exponent (according to the Calder\'on-Zygmund definition) of the Brjuno function $B$ everywhere, thus showing that it is a new example of multifractal function. We also discuss various notions of pointwise regularity of…
We study self-similar measures in $\mathbb{R}$ satisfying the weak separation condition along with weak technical assumptions which are satisfied in all known examples. For such a measure $\mu$, we show that there is a finite set of concave…
We study the local dimensions and local multifractal properties of measures on doubling metric spaces. Our aim is twofold. On one hand, we show that there are plenty of multifractal type measures in all metric spaces which satisfy only mild…
We undertake a general study of multifractal phenomena for functions. We show that the existence of several kinds of multifractal functions can be easily deduced from an abstract statement, leading to new results. This general approach does…
In this paper we use the theory of computing to study fractal dimensions of projections in Euclidean spaces. A fundamental result in fractal geometry is Marstrand's projection theorem, which shows that for every analytic set E, for almost…
Multifractal formalism is designed to describe the distribution at small scales of the elements of $\mathcal M^+_c(\R^d)$, the set of positive, finite and compactly supported Borel measures on $\R^d$. It is valid for such a measure $\mu$…
In this paper, we construct new multifractal measures, on the Euclidean space $\mathbb{R}^n$, in a similar manner to Hewitt-Stomberg measures but using the class of all $n$-dimensional half-open binary cubes of covering sets in the…
New proofs of theorems on the multifractal formalism are given. They yield results even at points q for which Olsen's functions b(q) and B(q) differ. Indeed, we provide an example of measure for which functions b and B differ and for which…
We refine the multifractal formalism for the local dimension of a Gibbs measure $\mu$ supported on the attractor $\Lambda$ of a conformal iterated functions system on the real line. Namely, for given $\alpha\in \mathbb{R}$, we establish the…
Multifractals are inhomogeneous measures (or functions) which are typically described by a full spectrum of real dimensions, as opposed to a single real dimension. Results from the study of fractal strings in the analysis of their geometry,…
In this paper, the notion of dimension preserving approximation for real-valued bivariate continuous functions, defined on a rectangular domain $\rectangle$, has been introduced and several results, similar to well-known results of…
We study multifractal properties in time evolution of a single particle subject to repeated measurements. For quantum systems, we consider circuit models consisting of local unitary gates and local projective measurements. For classical…
In this paper we study multi-parameter projection theorems for fractal sets. With the help of these estimates, we recover results about the size of $A \cdot A+...+A \cdot A$, where $A$ is a subset of the real line of a given Hausdorff…
We show that if $\mu$ is a self-affine measure on the plane defined by an iterated function system of contractions with diagonal linear parts, then under an irrationality assumption on the entries of the linear parts, $$ \dim_{\rm H} \mu…
We present an explicit formula for the orthogonal projection onto the subspace of analytic polynomials of degree at most $n$ in the local Dirichlet space $D_\mu$ , where the positive measure $\mu$ consists of a finite number of Dirac…