Related papers: Uniqueness theorems for Cauchy integrals

We study analytically the Cauchy horizon singularity inside spherically-symmetric charged black holes, coupled to a spherical self-gravitating, minimally-coupled, massless scalar field. We show that all causal geodesics terminate at the…

We continue our study of the reflectionless measures associated to an $s$-dimensional Calder\'{o}n-Zygmund operator (CZO) acting in $\mathbb{R}^d$ with $s\in (0,d)$. Here, our focus will be the study of CZOs that are rigid, in the sense…

A maxitive measure is the analogue of a finitely additive measure or charge, in which the usual addition is replaced by the supremum operation. Contrarily to charges, maxitive measures often have a density. We show that maxitive measures…

This paper is devoted to the proof of two related results. The first one asserts that if $\mu$ is a Radon measure in $\mathbb R^d$ satisfying $$\limsup_{r\to 0} \frac{\mu(B(x,r))}{r}>0\quad \text{ and }\quad…

Topological measures and deficient topological measures generalize Borel measures and correspond to certain non-linear functionals. We study integration with respect to deficient topological measures on locally compact spaces. Such an…

In this work, a mode of convergence for measurable functions is introduced. A related notion of Cauchy sequence is given and it is proved that this notion of convergence is complete in the sense that Cauchy sequences converge. Moreover, the…

For every frame spectral measure $ \mu $, there exists a discrete measure $ \nu $ as a frame measure. Since if $ \mu $ is not a frame spectral measure, then there is not any general statement about the existence of frame measures $ \nu $…

We consider the space $C_{\lambda}$ of all continuous interval maps preserving the Lebesgue measure $\lambda$. A continuous function $f\colon~[0,1]\to \mathbb R$ is called Besicovitch if it does not have any finite or infinite unilateral…

Let $u\not\equiv -\infty$ and $M\not\equiv -\infty$ are two subharmonic functions in the complex plane $\mathbb C$ with the Riesz measures $\nu_u$ and $\mu_M$ such that $u(z)\leq O(|z|)$ and $M(z)\leq O(|z|)$ as $z\to \infty$. If the growth…

A charge space $(X,\mathcal{A},\mu)$ is a generalisation of a measure space, consisting of a sample space $X$, a field of subsets $\mathcal{A}$ and a finitely additive measure $\mu$, also known as a charge. Key properties a real-valued…

For $1 \le t < \infty ,$ a compact subset $K$ of the complex plane $\mathbb C,$ and a finite positive measure $\mu$ supported on $K,$ $R^t(K, \mu)$ denotes the closure in $L^t (\mu )$ of rational functions with poles off $K.$ The paper…

We continue the study on Kurzweil--Stieltjes integration on compact lines initiated in [doi:10.1007/s11117-025-01161-9]. Given a real valued function $G$ on a compact line, the presented integral is called the Kurzweil--Stieltjes integral…

Let $K$ be a homogeneous self-similar set satisfying the strong separation condition. This paper is concerned with the quantitative recurrence properties of the natural map $T: K\rightarrow K$ induced by the shift. Let $\mu$ be the natural…

Let $G = (V,E)$ be a connected graph. A probability measure $\mu$ on $V$ is called "balanced" if it has the following property: if $T_\mu(v)$ denotes the "earth mover's" cost of transporting all the mass of $\mu$ from all over the graph to…

Let $f$ be a holomorphic automorphism of a compact K\"ahler manifold with simple action on cohomology and $\mu$ its unique measure of maximal entropy. We prove that $\mu$ is exponentially mixing of all orders for all d.s.h.\ observables,…

We prove that a singular part $\mu_s$ of a measure $\mu$ satisfying ${\cal A}\mu =0$ for a linear partial differential operator ${\cal A}$ defined on $R^d$ has the range in the intersection of kernels of the principal symbol of ${\cal A}$…

In this paper, we introduce the notion of a $\gamma$-density point for Lebesgue-measurable subsets of $\mathbb{R}$, where $\gamma$ is a modulus function, and study its basic measure-theoretic properties. We show that every $\gamma$-density…

Let $(\Omega,\Sigma,\mu)$ be a finite measure space, $Z$ be a Banach space and $\nu:\Sigma \to Z^*$ be a countably additive $\mu$-continuous vector measure. Let $X \subseteq Z^*$ be a norm-closed subspace which is norming for $Z$. Write…

Let $\mu$ be a self-similar measure satisfying the finite type condition. It is known that the set of attainable local dimensions for such a measure is a union of disjoint intervals, where some intervals may be degenerate points. Despite…

Consider an infinite sequence $(U_n)_{n\in\mathbb{N}}$ of independent Cauchy random variables, defined by a sequence $(\delta_n)_{n\in\mathbb{N}}$ of location parameters and a sequence $(\gamma_n)_{n\in\mathbb{N}}$ of scale parameters. Let…