Related papers: Equilibrium measures and partial balayage
The study deals with a minimal energy problem in the presence of an external field over noncompact classes of vector measures of infinite dimension in a locally compact space. The components are positive measures (charges) satisfying…
In this paper equilibrium measures in the presence of external fields created by fixed charges are analyzed. These external fields are a particular case of the so-called rational external fields (in the sense that their derivatives are…
We investigate some properties of balayage, or, sweeping (out), of measures with respect to subclasses of subharmonic functions. The following issues are considered: relationships between balayage of measures with respect to classes of…
In this note the logarithmic energy problem with external potential $|z|^{2n}+tz^d+\bar{t}\bar{z}^d$ is considered in the complex plane, where $n$ and $d$ are positive integers satisfying $d\leq 2n$. Exploiting the discrete rotational…
Equilibrium measures in the real axis in the presence of rational external fields are considered. These external fields are called rational since their derivatives are rational functions. We analyze the evolution of the equilibrium measure,…
We study the equilibrium measure for a logarithmic potential in the presence of an external field V*(x) + tp(x), where t is a parameter, V*(x) is a smooth function and p(x) a monic polynomial. When p(x) is of an odd degree, the equilibrium…
The purpose of this work is twofold. First, we aim to extend for $0<s<1$ the results of one of the authors about equilibrium measures in the real axis in external fields created by point-mass charges for the case of logarithmic potentials…
We prove existence and uniqueness of a solution to the problem of minimizing the logarithmic energy of vector potentials associated to a $d$-tuple of positive measures supported on closed subsets of the complex plane. The assumptions we…
We analyze the supports of weighted equilibrium measures in $\mathbb{C}^n$. We give explicit examples of families of compact sets which arise as the support of a weighted equilibrium measure for some admissible weight $w$. These examples…
Positivity violations, which occur when some subgroups either always or never receive a treatment of interest, pose significant challenges for causal effect estimation with observational data. Recent balancing weight methods have proved to…
We explore the connection between supports of equilibrium measures and quadrature identities, especially in the case of point sources added to the external field $Q(z)=|z|^{2p}$ with $p \in \mathbb{N}$. Along the way, we describe some…
We provide a generalized definition of polygamy relations for any quantum correlation measures. Instead of the usual polygamy inequality, a polygamy relation with equality is given by introducing the polygamy weight. From the polygamy…
We investigate some properties of balayage of charges and measures for subclasses of subharmonic functions and their relationship to the geometry of domain or open set in finite-dimensional Euclidean space where this balayage is considered.
It is a well-known conjecture in $\beta$-models and in their discrete counterpart that, generically, external potentials should be ``off-critical'' (or, equivalently, ``regular''). Exploiting the connection between minimizing measures and…
We use Pesin theory to study possible equilibrium measures for piecewise monotone maps of the interval. The maps may have unbounded derivative.
This work concerns superharmonic perturbations of a Gaussian measure given by a special class of positive weights in the complex plane of the form $w(z) = \exp(-|z|^2 + U^{\mu}(z))$, where $U^{\mu}(z)$ is the logarithmic potential of a…
The paper deals with the theory of inner (outer) capacities on locally compact spaces with respect to general function kernels, the main emphasis being placed on the establishment of alternative characterizations of inner (outer) capacities…
The main subject of this paper is equilibrium problems on an unbounded conductor $\Sigma$ of the complex plane in the presence of a weakly admissible external field. An admissible external field $Q$ on $\Sigma$ satisfies, along with other…
We study the monogamy and polygamy relations related to quantum correlations for multipartite quantum systems in a unified manner. It is known that any bipartite measure obeys monogamy and polygamy relations for the $r$-power of the…
We propose a formal resource theoretic approach to asses the coherence between partially polarized electromagnetic fields. We show that naturally defined incoherent operations endow partial coherence with a preorder relation that must be…