Related papers: Weakly controlled Moran constructions and iterated…
The (e,n)-complexity functions describe total instability of trajectories in dynamical systems. They reflect an ability of trajectories going through a Borel set to diverge on the distance $\epsilon$ during the time interval n. Behavior of…
We characterize the subsets $E$ of a metric space $X$ with doubling measure whose distance function to some negative power $\textrm{dist}(\cdot,E)^{-\alpha}$ belongs to the Muckenhoupt $A_1$ class of weights in $X$. To this end, we…
Following Semmes and Zinsmeister, we continue the study of Carleson measures and their invariance under pull-back and push-forward operators. We also study the analogous statements for vanishing Carleson measures. As an application, we show…
In this study, we investigate the boundedness of composition operators acting on Morrey spaces and weak Morrey spaces. The primary aim of this study is to investigate a necessary and sufficient condition on the boundedness of the…
We determine the extent to which certain classes of fractionally `smooth' continuous mappings between metric spaces distort various dimensions, including the Hausdorff, upper Minkowski (box-counting), and upper intermediate dimensions. Our…
We develop the local Morse theory for a class of non-twice continuously differentiable functionals on Hilbert spaces, including a new generalization of the Gromoll-Meyer's splitting theorem and a weaker Marino-Prodi perturbation type…
We investigate the power of weak measurements in the framework of quantum state discrimination. First, we define and analyze the notion of weak consecutive measurements. Our main result is a convergence theorem whereby we demonstrate when…
Weak measurement is a novel quantum measurement scheme, which is usually characterized by the weak value formalism. To guarantee the validity of the weak value formalism, the fidelity between the pre-selection and the post-selection should…
Intermediate dimensions are a class of new fractal dimensions which provide a spectrum of dimensions interpolating between the Hausdorff and box-counting dimensions. In this paper, we study the intermediate dimensions of Moran sets. Moran…
In this article, we provide a simple and systematic way to represent general (inhomogeneous) fractals that may look different at different scales and places. By using set-valued compression maps, we express these general fractals as…
Consider the lattice of bounded linear operators on the space of Borel measures on a Polish space. We prove that the operators which are continuous with respect to the weak topology induced by the bounded measurable functions form a…
Continuous time branching models are used to create random fractals in a Euclidean space, whose Hausdorff dimension is controlled by an input parameter. Finite realizations are applied in modelling the set of sites visited in models of…
We consider Lorentzian manifolds as examples of partially ordered measure spaces, sets endowed with compatible partial order relations and measures, in this case given by the causal structure and the volume element defined by each…
In this article, we study the Hausdor dimension of weakly conformal IFS's shrinking targets with possible overlaps, provided the conformality dimension of the systems and the dimension of the attractor are equal. Those results extends the…
The method of iterated conformal maps allows to study the harmonic measure of Diffusion Limited Aggregates with unprecedented accuracy. We employ this method to explore the multifractal properties of the measure, including the scaling of…
The triangular ratio metric is studied in subdomains of the complex plane and Euclidean $n$-space. Various inequalities are proven for it. The main results deal with the behavior of this metric under quasiconformal maps. We also study the…
We study the effect of spatial inhomogeneity on the physics of a strongly correlated electron system exhibiting a metallic phase and a Mott insulating phase, represented by the simple Hubbard model. In three dimensions, we consider various…
Fourier-transformable Radon measures are called doubly sparse when both the measure and its transform are pure point measures with sparse support. Their structure is reasonably well understood in Euclidean space, based on the use of…
In many low-dimensional dynamical systems transport coefficients are very irregular, perhaps even fractal functions of control parameters. To analyse this phenomenon we study a dynamical system defined by a piece-wise linear map and…
In the first part, we construct a cut and project scheme from a family $\{P_\varepsilon\}$ of sets verifying four conditions. We use this construction to characterize weighted Dirac combs defined by cut and project schemes and by continuous…