Related papers: Multifractal phenomena and packing dimension
We introduce multifractal pressure and dynamical multifractal zeta-functions providing precise information of a very general class of multifractal spectra, including, for example, the fine multifractal spectra of self-conformal measures and…
This work is an extension of the incomplete probability theory from the simple case of monofractals previously studied to the more general case of multifractals which can occur in the phase space without equiprobable partition.
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…
This paper develops an analytic theory of Dirichlet series in several complex variables which possess sufficiently many functional equations. In the first two sections it is shown how straightforward conjectures about the meromorphic…
Various methods have been developed independently to study the multifractality of measures in many different contexts. Although they all convey the same intuitive idea of giving a "dimension" to sets where a quantity scales similarly within…
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 paper introduces a new concept of $\Lambda $-variation of multivariable functions and investigates its connection with the convergence of multidimensional Fourier series
We study regularity properties of frequency measures arising from random substitutions, which are a generalisation of (deterministic) substitutions where the substituted image of each letter is chosen independently from a fixed finite set.…
We describe singular diffusion in bounded subsets $\Omega$ of $\mathbb{R}^n$ by form methods and characterize the associated operator. We also prove positivity and contractivity of the corresponding semigroup. This results in a description…
In this paper Fourier transform of multivariate orthogonal polynomials on the simplex is presented. A new family of multivariate orthogonal functions is obtained by using the Parseval's identity and several recurrence relations are derived.
We consider multifractal Mandelbrot cascades supported on planar $C^2$ curves with nonvanishing curvature and show that their Fourier dimension is as large as possible, i.e., equal to the infimum of the lower pointwise dimension of the…
We compute the typical (in the sense of Baire's category theorem) multifractal box dimensions of measures on a compact subset of $\mathbb R^d$. Our results are new even in the context of box dimensions of measures.
We obtain an exact formula for the Fourier transform of multiradial functions, i.e., functions of the form $\Phi(x)=\phi(|x_1|, \dots, |x_m|)$, $x_i\in \mathbf R^{n_i}$, in terms of the Fourier transform of the function $\phi$ on $\mathbf…
The analysis of multi-dimensional graph signals on complex structured domains remains a fundamental challenge,
In view of the role of reaction equations in physical problems, the authors derive the explicit solution of a fractional reaction equation of general character, that unifies and extends earlier results. Further, an alternative shorter…
A mathematical relation between elements of one- and multi-dimensional discrete Fourier transforms (DFT) is found. A method of analysing the multi-dimensional data by their single one-dimensional (1-D) DFT is offered. An experiment of…
The construction of a multiresolution analysis starts with specification of a scale function. The Fourier transform of this function is defined by an infinite product. The convergence of this product is usually discussed in the context of…
The aim of this article is to study the behaviour of the multifractal packing function $B_\mu(q)$ under projections in Euclidean space for $q>1$. We show that $B_\mu(q)$ is preserved under almost every orthogonal projection. As an…
In this note, we study the general form of a multiplicative bijection on several families of functions defined on manifolds, both real or complex valued. In the real case, we prove that it is essentially defined by a composition with a…
The notion of wavelets is defined. It is briefly described {\it what} are wavelets, {\it how} to use them, {\it when} we do need them, {\it why} they are preferred and {\it where} they have been applied. Then one proceeds to the…