Related papers: Green vs. Lempert functions: a minimal example

This paper studies the uniqueness of two non-integral finite ordered meromorphic functions with finitely many poles when they share two finite sets. Also, studies an answer to a question posed by Gross for a particular class of meromorphic…

We prove that the Green equilibrium measure and the Green equilibrium energy of a compact set K relative to the domains D and G are the same if and only if D is nearly equal to G, for a wide class of compact sets K. Also, we prove that…

We study questions related to critical points of the Green's function of a bounded multiply connected domain in the complex plane. The motion of critical points, their limiting positions as the pole approaches the boundary and the…

A method to calculate exact Green's functions on lattices in various dimensions is presented. Expressions in terms of generalized hypergeometric functions in one or more variables are obtained for various examples by relating the resolvent…

Asymptotically sharp Bernstein- and Markov-type inequalities are established for rational functions on $C^2$ smooth Jordan curves and arcs. The results are formulated in terms of the normal derivatives of certain Green's functions with…

In the plane, we consider the problem of reconstructing a domain from the normal derivative of its Green's function (with fixed pole) relative to the Dirichlet problem for the Laplace operator. By means of the theory of conformal mappings,…

We study the Green function for the stationary Stokes system with bounded measurable coefficients in a bounded Lipschitz domain $\Omega\subset \mathbb{R}^n$, $n\ge 3$. We construct the Green function in $\Omega$ under the condition…

In this paper, we construct a family of generalized $L$-functions, one for each point $z$ in the upper half-plane. We prove that as $z$ approaches $i\infty$, these generalized $L$-functions converge to an $L$-function which can be written…

Given a system of functions $\textup{\textbf{F}}=(F_1,\ldots,F_d),$ analytic on a neighborhood of some compact subset $E$ of the complex plane with simply connected complement, we define a sequence of vector rational functions with common…

Leibniz' combinatorial formula for determinants is modified to establish a condensed and easily handled compact representation for Hessenbergians, referred to here as Leibnizian representation. Alongside, the elements of a fundamental…

Larman showed that any closed subset of the plane with uncountable vertical cross-sections has aleph_1 disjoint Borel uniformizing sets. Here we show that Larman's result is best possible: there exist closed sets with uncountable…

Let $u\not\equiv -\infty$ be a subharmonic function on the complex plane $\mathbb C$. Then for any function $r\colon\mathbb C\to (0,1]$ satisfying the condition $$\inf_{z\in\mathbb C}\frac{\ln r(z)}{\ln(2+|z|)}>-\infty,$$ there is an entire…

Let $\mathcal R_{n}$ be the set of all rational functions of the type $r(z) = f(z)/w(z)$, where $f(z)$ is a polynomial of degree at most $n$ and $w(z) = \prod_{j=1}^{n}(z-\beta_j)$, $|\beta_j|>1$ for $1\leq j\leq n$. In this work, we…

A formulation of the Green's function method is presented in the n-pole approximation. Without referring to a specific model we give a general scheme of calculations that easily permits the computation of the "single-particle" Green's…

In this paper we generalize the classical theorems of Brown and Halmos about algebraic properties of Toeplitz operators to Bergman spaces over the unit ball in several complex variables. A key result, which is of independent interest, is…

We state and prove a Lemma in 1 variable Calculus, that justifies some arguments previously used to ilustrate non-uniqueness of some generalized physical quantities.

It is known that Shintani zeta functions, which generalise multiple zeta functions, extend to meromorphic functions with poles on affine hyperplanes. We refine this result in showing that the poles lie on hyperplanes parallel to the facets…

We show that the coefficients of rational 2-functions are contained in an abelian number field. More precisely, we show that the poles of such functions are poles of order one and given by roots of unity and rational residue.

A point charge between the plates of a capacitor generates an influence charge distribution on the plates that modify the electric field acting upon the point charge. This effect is described by the well-known Dirichlet Green's function for…

Finite collections of point masses contained in some bounded domain produce a unique field in the exterior domain, which means that the associated basis functions (often called ``fundamental solutions'') are independent. A new proof of this…