Avetisyan, K. L.
Published in
Lobachevskii Journal of Mathematics

Boundedness of some Poisson-Bergman type operators is stated over the unit ball in ℝn. Forelli-Rudin type theorems are proved and bounded harmonic projections are found on Lipschitz and mixed norm spaces.

Petrosyan, A. I.
Published in
Lobachevskii Journal of Mathematics

We introduce the Banach spaces h∞(ϕ), h0(ϕ) and h1(ψ) functions harmonic in the unit ball B ⊂ ℝn. These spaces depend on weight functions ϕ, ψ. We prove that if ϕ and ψ form a normal pair, then h1(ψ)* ∼ h∞(ϕ) and h0(ϕ)* ∼ h1(ψ).

wang, minqiu yin, songting

We give some Liouville type theorems of L p harmonic (resp. subharmonic, superharmonic) functions on a complete noncompact Finsler manifold. Using the geometric relationship between a Finsler metric and its reverse metric, we remove some restrictions on the reversibility. These improve the recent literature (Zhang and Xia, 2014).

yin, songting

We prove that in Minkowski spaces, a harmonic function does not necessarily satisfy the mean value formula. Conversely, we also show that a function satisfying the mean value formula is not necessarily a harmonic function. Finally, we conclude that in a Minkowski space, if all harmonic functions have the mean value property or any function satisfyi...

Kokurin, M. Yu.
Published in
Mathematical Notes

It is proved that the family of all pairwise products of regular harmonic functions on D and of the Newtonian potentials of points on the line L ⊂ Rn is complete in L2(D), where D is a bounded domain in Rn, n ≥ 3, such that D¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepacka...

guariglia, emanuel

nyi entropy, their performance is characterized by the associated entropy that is studied and discussed here.

Subbotin, Yu. N. Chernykh, N. I.
Published in
Proceedings of the Steklov Institute of Mathematics

We propose and validate a simple numerical method that finds an approximate solution with any given accuracy to the Dirichlet boundary value problem in a disk for a homogeneous equation with the Laplace operator. There are many known numerical methods that solve this problem, starting with the approximate calculation of the Poisson integral, which ...

Grama, Ion Lauvergnat, Ronan Le Page, Emile

Consider the real Markov walk $S_n = X_1+ \dots+ X_n$ with increments $\left(X_n\right)_{n\geqslant 1}$ defined by a stochastic recursion starting at $X_0=x$. For a starting point $y>0$ denote by $\tau_y$ the exit time of the process $\left( y+S_n \right)_{n\geqslant 1}$ from the positive part of the real line. We investigate the asymptotic behavio...

Abid, Jamel

Using algebraic methods, we prove that there exists a fundamental relation between partial differential equations and strictly plurisubharmonic functions over domains of Cn(n ≥ 1).

Grama, Ion Lauvergnat, Ronan Le Page, Emile

Consider a Markov chain (X n) n0 with values in the state space X. Let f be a real function on X and set S 0 = 0, S n = f (X 1) + · · · + f (X n), n 1. Let P x be the probability measure generated by the Markov chain starting at X 0 = x. For a starting point y ∈ R denote by τ y the first moment when the Markov walk (y + S n) n1 becomes non-positive...