Related papers: Balayage of measures on a locally compact space

We introduce a new optimal transport distance between nonnegative finite Radon measures with possibly different masses. The construction is based on non-conservative continuity equations and a corresponding modified Benamou-Brenier formula.…

The theorems of M. Ratner, describing the finite ergodic invariant measures and the orbit closures for unipotent flows on homogeneous spaces of Lie groups, are extended for actions of subgroups generated by unipotent elements. More…

The paper deals with minimum energy problems in the presence of external fields on a locally compact space $X$ with respect to a function kernel $\kappa$ satisfying the energy and consistency principles. For quite a general (not necessarily…

We study the regularity of Radon measures $\mu$ which satisfy that there exists a function $h_\mu$ in $H^1(\Omega)$, stationary harmonic such that $\Delta h_\mu =\mu$ in $\Omega$ (here $\Omega$ is an open set of $\mathbb{R}^2$). Such…

The Laplace transforms of positive measures on $\mathbb{R}_{+}$ converge if and only if their distribution functions converge at continuity points of the limiting measure. We extend this classical continuity theorem to the case of…

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…

We expand the classical balayage of measures and subharmonic functions on a system of rays $S$ with a common origin on the complex plane $\mathbb C$. This allows for an arbitrary subharmonic function $v$ of finite order on $\mathbb C$ build…

Let $\L$ be a Schr\"odinger operator of the form $\L=-\Delta+V$ acting on $L^2(\mathbb R^n)$, $n\geq3$, where the nonnegative potential $V$ belongs to the reverse H\"older class $B_q$ for some $q\geq n.$ Let ${\rm BMO}_{{\mathcal{L}}}(\RR)$…

We develop and use some key concepts of potential theory, such as balayage and duality between measures and their potentials, to study the distribution of masses of subharmonic functions while restrictions to their growth near the boundary…

We present additional observations to previous studies on the infrared (IR) renormalon in $SU(N)$ QCD(adj.), the $SU(N)$ gauge theory with $n_W$-flavor adjoint Weyl fermions on~$\mathbb{R}^3\times S^1$ with the $\mathbb{Z}_N$ twisted…

Let $X$ be a quasi-Banach space of analytic functions in the unit disc and let $q>0$. A finite positive Borel measure $\mu$ in the closed unit disc $\overline{\mathbb{D}}$ is called a $q$-reverse Carleson measure for $X$ if and only if…

The paper deals with minimum energy problems in the presence of external fields with respect to the Riesz kernels $|x-y|^{\alpha-n}$, $0<\alpha<n$, on $\mathbb R^n$, $n\geqslant2$. For quite a general (not necessarily lower semicontinuous)…

We prove an analogue of the portmanteau theorem on weak convergence of probability measures allowing measures which are unbounded on an underlying metric space but finite on the complement of any Borel neighbourhood of a fixed element.

Given a Radon probability measure $\mu$ supported in $\mathbb{R}^d$, we are interested in those points $x$ around which the measure is concentrated infinitely many times on thin annuli centered at $x$. Depending on the lower and upper…

Given a compact metric space $X$, the collection of Borel probability measures on $X$ can be made into a compact metric space via the Kantorovich metric. We partially generalize this well known result to projection-valued measures. In…

Motivated by recent investigations of Sophie Grivaux and \'Etienne Matheron on the existence of invariant measures in Linear Dynamics, we introduce the concept of locally bounded orbit for a continuous linear operator $T:X\longrightarrow X$…

We consider the family of harmonic measures on a lamination $\mathcal{L}$ of a compact space $X$ by locally symmetric spaces $L$ of noncompact type, i.e. $L\simeq \Gamma_L\backslash G/K$. We establish a natural bijection between these…

Let $X$ be a locally compact Polish space. Let $\mathbb K(X)$ denote the space of discrete Radon measures on $X$. Let $\mu$ be a completely random discrete measure on $X$, i.e., $\mu$ is (the distribution of) a completely random measure on…

We establish a good lambda inequality relating to the distribution function of Riesz potential and fractional maximal function on $\left(\mathbb{R}^n, d\mu\right)$ where $\mu$ is a positive Radon measure which doesn't necessarily satisfy a…

We develop a measure and integration theory for random normed modules. Given a probability space $({\rm X},\Sigma,\mathfrak m)$, we introduce and study measures taking values into the space $L^0(\mathfrak m)$ of $\mathfrak m$-measurable…