Related papers: On the product property of the pluricomplex Green …
Generating functions and functional equations of Dickson polynomials of the first and second kind are derived and continued analytically. These formulae are expressed in terms of the incomplete gamma function over complex variables of the…
In the paper we prove for every finite algebra A that either it has the polynomially generated powers (PGP) property, or it has the exponentially generated powers (EGP) property. For idempotent algebras we give a simple criteria for the…
Let $D$ be a bounded strongly convex domain in the complex space of dimension $n$. Fixed a point $p\in \partial D$, we consider the solution of a homogeneous complex Monge-Ampere equation with simple pole at $p$. We prove that such a…
We present an experiment which aim is to investigate the mechanical properties of a static granular assembly. The piling is an horizontal 3D granular layer confined in a box, we apply a localized extra force at the surface and the spatial…
We study pluricomplex Green functions on algebraic sets. Let $f$ be a proper holomorphic mapping between two algebraic sets. Given a compact set $K$ in the range of $f$, we show how to estimate the pluricomplex Green functions of $K$ and of…
We consider the notion of the graph product of actions of groups $\left\{G_v\right\}$ on a $C^*$-algebra $\mathcal{A}$ and show that under suitable commutativity conditions the graph product action $\bigstar_\Gamma \alpha_v: \bigstar_\Gamma…
We study inequalities for the infima of Green potentials on a compact subset of an arbitrary domain in the complex plane. The results are based on a new representation of the pseudohyperbolic farthest-point distance function via a Green…
We extend some results on piecewise linear functions on $\C^n$ to piecewise pluriharmonic functions on any complex manifold. We construct a ring generated by currents $h$ and $dd^ch$, where $\{h\}$ is a finite set of piecewise pluriharmonic…
We consider bicrossed products obtained by twisting compact semi-direct products by a suitable finite subgroup. Under some restriction, we give a practical criterion for the discrete dual of such bicrossed products to have the rapid decay…
We characterize infinitesimal generators of semigroups of holomorphic self-maps of strongly convex domains using the pluricomplex Green function and the pluricomplex Poisson kernel. Moreover, we study boundary regular fixed points of…
In this note we establish the positivity of Green's functions for a class of elliptic differential operators on closed, Riemannian manifolds.
We show that Green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. Higher order corrections can be then computed giving a satisfactory agreement with…
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…
In this short article, we non-perturbatively derive a recursive formula for the Green's function associated with finitely many point Dirac delta potentials in one dimension. We also extend this formula to the case for the Dirac delta…
We determine all maximal subgroups of the direct product $\sc G^n$ of $\sc n$ copies of a group~$\sc G$. If $\sc G$ is finite, we show that the number of maximal subgroups of~$\sc G^n$ is a quadratic function of~$\sc n$ if $\sc G$ is…
We construct Green functions of conormal derivative problems for the stationary Stokes system with measurable coefficients in a two dimensional Reifenberg flat domain.
We demonstrate that the effective Hamiltonians obtained with the downfolding procedure based on double unitary coupled cluster (DUCC) ansatz can be used in the context of Greens function coupled cluster (GFCC) formalism to calculate…
The celebrated theorem of Gromov asserts that any finitely generated group with polynomial growth contains a nilpotent subgroup of finite index. Alternative proofs have been given by Kleiner and others. In this note, we give yet another…
Let V_E be the pluricomplex Green function associated to a compact subset E of C^N. The well known H\"older Continuity Property of E means that there exist constants B > 0, 0< c =< 1 such that V_E(z) =< B dist(z,E)^c. The main result of…
This paper is concerned with the study of Green's functions for one dimensional diffusions with constant diffusion coefficient and linear time inhomogeneous drift. It is well know that the whole line Green's function is given by a Gaussian.…