Related papers: Poisson-Jensen Formulas and Balayage of Measures
Recently the authors have explored new concepts of plurisubharmonicity and pseudoconvexity, with much of the attendant analysis, in the context of calibrated manifolds. Here a much broader extension is made. This development covers a wide…
In this paper, we present some double inequalities involving certain ratios of the Gamma function. These results are further generalizations of several previous results. The approach is based on the monotonicity properties of some functions…
We devise variants of classical nonconforming methods for symmetric elliptic problems. These variants differ from the original ones only by transforming discrete test functions into conforming functions before applying the load functional.…
The fidelity (Shannon mutual information between measurements and physical quantities) is proposed as a quantitative measure of the quality of physical measurements. The fidelity does not depend on the true value of unknown physical…
Let $\psi:{\mathcal{D}}\rightarrow{\mathbf{R}}$ be a harmonic function such that $\Delta\psi(x)=0$ for all $x\in\mathcal{D}\subset{\mathbf{R}}^{n}$. There are then many well-established classical results:the Dirichlet problem and Poisson…
We study new Legendre transforms in classical mechanics and investigate some of their general properties. The behaviour of the new functions is analyzed under coordinate transformations.When invariance under different kinds of…
In this pedagogically structured article, we describe a generalized harmonic formulation of the Einstein equations in spherical symmetry which is regular at the origin. The generalized harmonic approach has attracted significant attention…
This work is dedicated to foundational aspects of general (nonlinear second order) potential theories and fully nonlinear elliptic PDEs. In particular, we systematically develop the fundamental role played by semiconvex functions as a…
Energy-dependent Green's functions for the two and three dimensional $\delta$-function plus harmonic oscillator potential systems are derived by incorporating the renormalization and the self-adjoint extension into the Green's function…
We prove that a Poisson-Newton formula, in a broad sense, is associated to each Dirichlet series with a meromorphic extension to the whole complex plane of finite order. These formulas simultaneously generalize the classical Poisson formula…
Reduction is shown to be a possible consequence of the basic principles of quantum mechanics, involving no branching of the quantum state of the universe. The key feature of a measurement is attributed to the creation of macroscopic germs…
We study two techniques to obtain new families of classical and general Dual-Feasible Functions: A conversion from minimal Gomory--Johnson functions; and computer-based search using polyhedral computation and an automatic maximality and…
Wavefunction correlations and density matrices for few or many particles are derived from the properties of semiclassical energy Green functions. Universal features of fixed energy (microcanonical) random wavefunction correlation functions…
We extend the functional Breuer-Major theorem for Gaussians to the Poisson case, where the stationary sequence arises from a Poisson point process. We use the $L^p$ spectral gap inequality of Poisson point process as a tool to prove…
The aim of the paper is to introduce an alternative notion of two-scale convergence which gives a more natural modeling approach to the homogenization of partial differential equations with periodically oscillating coefficients: while…
We study the convex cone of not necessarily smooth measures satisfying the classical KMS condition within the context of Poisson geometry. We discuss the general properties of KMS measures and its relation with the underlying Poisson…
First, we give the definition for quasi-nearly subharmonic functions, now for general, not necessarily nonnegative functions, unlike previously. We point out that our function class incudes, among others, quasisubharmonic functions, nearly…
We present versions of several classical results on harmonic functions and Poisson boundaries in the setting of locally compact quantum groups. In particular, the Choquet--Deny theorem holds for compact quantum groups; also, the result of…
We briefly describe some well-known means and their properties, focusing on the relationship with integer sequences. In particular, the harmonic numbers, deriving from the harmonic mean, motivate the definition of a new kind of mean that we…
We supplement the result of the first part of the work with estimates of the integrals of the difference of subharmonic functions in measure with some deterioration of the absolute constants, but these estimates have the form of a…