Related papers: Discrete Uniqueness Sets for Functions with Spectr…

We establish sufficient conditions on discrete subsets of $\mathbb{R}^d$ for them to form a uniqueness or a non-uniqueness pair for the fractional Laplacian. Specifically, assuming that $f=0$ on $\Lambda$ and that $(-\Delta)^sf=0$ on $M$,…

The paper is concerned with random $S$-adic systems arising from an i.i.d. sequence of unimodular substitutions. Using equidistribution results of Benoist and Quint, we show in Theorem 3.3 that, under some natural assumptions, if the…

We introduce the notion of \emph{joint spectrum} of a compact set of matrices $S \subset GL_d(\mathbb{C})$, which is a multi-dimensional generalization of the joint spectral radius. We begin with a thorough study of its properties (under…

Periodic point sets model all solid crystalline materials whose structures are determined in a rigid form and should be studied up to rigid motion or isometry preserving inter-point distances. In 2021 H.Edelsbrunner et al. introduced an…

We introduce an interesting method of proving separable reduction theorems - the method of elementary submodels. We are studying whether it is true that a set (function) has given property if and only if it has this property with respect to…

We show that there exists a family of mutually singular doubling measures on Laakso space with respect to which real-valued Lipschitz functions are almost everywhere differentiable. This implies that there exists a measure zero universal…

We prove that when $f$ is a continuous selfmap acting on compact metric space $(X,d)$ which satisfies the shadowing property, then the set of irregular points (i.e. points with divergent Birkhoff averages) has full entropy. Using this fact…

We prove that intersections and unions of independent random sets in finite spaces achieve a form of Lipschitz continuity. More precisely, given the distribution of a random set $\Xi$, the function mapping any random set distribution to the…

We prove the spectral gap property for random walks on the product of two non-locally isomorphic analytic real or p-adic compact groups with simple Lie algebras, under the necessary condition that the marginals posses a spectral gap.…

Let $D$ be a bounded domain in ${\Bbb R}^n$ whose boundary has a Minkowski dimension $\alpha<n$. Suppose that $E_{\Lambda}= {\{e^{2 \pi i x \cdot \lambda}\}}_{\lambda \in \Lambda}$, $\Lambda$ an infinite discrete subset of ${\Bbb R}^n$, is…

We prove that the completely irregular set is Baire generic for every non-uniquely ergodic transitive continuous map which satisfies the shadowing property and acts on a compact metric space without isolated points. We also show that, under…

We study the mean-value harmonic functions on open subsets of $\mathbb{R}^n$ equipped with weighted Lebesgue measures and norm induced metrics. Our main result is a necessary condition saying that all such functions solve a certain…

The concept of a uniform set is introduced for an ergodic, measure-preserving transformation on a non-atomic, infinite Lebesgue space. The uniform sets exist as much as they generate the underlying $\sigma$-algebra. This leads to the result…

We investigate tiling properties of spectra of measures, i.e., sets $\Lambda$ in $\br$ such that $\{e^{2\pi i \lambda x}: \lambda\in\Lambda\}$ forms an orthogonal basis in $L^2(\mu)$, where $\mu$ is some finite Borel measure on $\br$. Such…

A subset of a discrete group $G$ is called completely Sidon if its span in $C^*(G)$ is completely isomorphic to the operator space version of the space $\ell_1$ (i.e. $\ell_1$ equipped with its maximal operator space structure). We recently…

This article investigates the phenomenon of maximal rigidity in spatial processes, where perfect interpolation of the process is possible from partial information, specifically, from its restriction to a strict subdomain, often resulting in…

We show the existence of singular inner functions that are cyclic in some Besov-type spaces of analytic functions over the unit disc. Our sufficient condition is stated only in terms of the modulus of smoothness of the underlying measure.…

This paper is devoted to study stability of Lyapunov exponents and simplicity of Lyapunov spectrum for bounded random compact operators on a separable infinite-dimensional Hilbert space from a generic point of view generated by the…

We construct a uniformly discrete sequence $\{\lambda_1 < \lambda_2 < \cdots\} \subset \mathbb{R}$ and functions $g$ and $\{g_n^*\}$ in $L^2(\mathbb{R})$, such that every $f \in L^2(\mathbb{R})$ admits a series expansion \[ f(x) =…

We study sublevel set and superlevel set persistent homology on discrete functions through the perspective of finite ordered sets of both linearly ordered and cyclically ordered domains. Finite ordered sets also serve as the codomain of our…