相关论文: Poisson-Jensen Formulas and Balayage of Measures

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 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…

We study mean value properties of harmonic functions in metric measure spaces. The metric measure spaces we consider have a doubling measure and support a (1,1)- Poincar\'e inequality. The notion of harmonicity is based on the Dirichlet…

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.

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…

We develop classical balayage (sweeping) measures and subharmonic functions on the ray system $S$ with a general origin on the complex plane $\mathbb C$. This allows for a subharmonic function $v$ on $\mathbb C$ to construct also a…

This paper extends the asymmetric Kullback-Leibler divergence and symmetric Jensen-Shannon divergence from two probability measures to the case of two sets of probability measures. We establish some fundamental properties of these…

We construct and apply the classic balayage (sweeping out) of measures and subharmonic functions on closed system of rays in the complex plane with vertex at the origin, including measures and subharmonic functions and infinite order. The…

We prove the existence and study properties of the Green function of the unit ball for the Dunkl Laplacian $\Delta_k$ in $\mathbb{R}^d$. As applications we derive the Poisson-Jensen formula for $\Delta_k$-subharmonic functions and…

Our starting point is the measure $\epsilon_x-\alpha_x\rho_x^{\omega_1}+\beta_x\rho_x^{\omega_2}$, where $\rho_x^{\omega_i}$ is the harmonic measure relative to $x \in \omega_1 \subset \overline{\omega}_1 \subset \omega_2$ and $\omega_i$…

This paper presents a novel framework for enclosing solutions of Poisson's equation based on generalized sub- and super-solutions constructed using fundamental solutions. The conventional definition of sub- and super-solutions based on…

This document presents the statistical methods used to process low-level measurements in the presence of noise. These methods can be classical or Bayesian. The question is placed in the general framework of the problem of nuisance…

We introduce and develop the notion of spherical polyharmonics, which are a natural generalisation of spherical harmonics. In particular we study the theory of zonal polyharmonics, which allows us, analogously to zonal harmonics, to…

Balayage of measures with respect to classes of all subharmonic or harmonic functions on an open set of a plane or finite-dimensional Euclidean space is one of the main objects of potential theory and its applications to the complex…

It is shown that, for open sets in classical potential theory and - more generally - for elliptic harmonic spaces, the set of Jensen measures for a point is a simple union of closed faces of a compact convex set which has been thoroughly…

In the framework of the generalized measure theory the decomposable probabilistic-valued set functions are introduced with triangle functions $\tau$ in an appropriate probabilistic metric space as natural candidates for the "addition",…

We extend the notion of quasibounded harmonic functions to the plurisubharmonic setting. As an application, using the theory of Jensen measures, we show that certain generalized Dirichlet problems with unbounded boundary data admit unique…

Classical and quantum measurement theories are usually held to be different because the algebra of classical measurements is commutative, however the Poisson bracket allows noncommutativity to be added naturally. After we introduce…

We give a characterization of harmonic and subharmonic functions in terms of their mean values in balls and on spheres. This includes the converse of an inequality of Beardon's for subharmonic functions. We also obtain integral inequalities…

Arithmetic, geometric and harmonic means are the three classical means famous in the literature. Another mean such as square-root mean is also known. In this paper, we have constructed divergence measures based on nonnegative differences…