Related papers: Powers of Brownian Green Potentials
In this paper, we study the stability of general kernel bundles on $\mathbb{P}^n$. Let $a,b,d>0$ be integers. A kernel bundle $E_{a,b}$ on $\mathbb{P}^n$ is defined as the kernel of a surjective map…
We study scalar perturbations to a Robertson-Walker cosmological metric in terms of a pseudo-Newtonian potential, which emerges naturally from the solution of the field equations. This potential is given in terms of a Green function for…
The purpose of this paper is to find optimal estimates for the Green function and the Poisson kernel for a half-line and intervals of the geometric stable process with parameter $\alpha\in(0,2]$. This process has an infinitesimal generator…
We examine the one-dimensional quantum dynamics of a Schroedinger particle in a potential represented by a generalized function of the form $U(x) = -\alpha \delta (x) + \beta d(\delta (x))/dx$ superposed on a well behaved potential $V(x)$.…
We introduce a class of embedded CR manifolds satisfying a geometric condition that we call weak $Y(q)$. For such manifolds, we show that dbar-b has closed range on $L^2$ and that the complex Green operator is continuous on $L^2$. Our…
Motivated by recent experimental refinements of stellar reaction rates, we establish a non-perturbative Green's function formalism based on the exact solution of the Dyson equation for sub-barrier proton-nucleus resonant scattering. By…
In this work, we present a new result which concerns the derivation of the Green function relative to the time-independent Schrodinger equation in two dimensional space. The system considered in this work is a quantum particle that have an…
We consider the convolution equation $(\delta - J) * G = g$ on $\mathbb R^d$, $d>2$, where $\delta$ is the Dirac delta function and $J,g$ are given functions. We provide conditions on $J, g$ that ensure the deconvolution $G(x)$ to decay as…
We study the low-energy behavior of the Green function for one-dimensional Fokker-Planck and Schr\"odinger equations with periodic potentials. We derive a formula for the power series expansion of reflection coefficients in terms of the…
The low-energy structure and $\beta$ decay properties of the neutron-rich even-mass nuclei near the neutron number $N=60$ that are experimentally of much interest are investigated within the framework of the nuclear density functional…
To convert standard Brownian motion $Z$ into a positive process, Geometric Brownian motion (GBM) $e^{\beta Z_t}, \beta >0$ is widely used. We generalize this positive process by introducing an asymmetry parameter $ \alpha \geq 0$ which…
We study properties of weighted Szeg\H{o} and Garabedian kernels on planar domains. Motivated by the unweighted case as explained in Bell's work, the starting point is a weighted Kerzman-Stein formula that yields boundary smoothness of the…
We derive explicit representation formulae of Green functions for GJMS operators on $n$-spheres, including the fractional ones. These formulae have natural geometric interpretations concerning the extrinsic geometry of the round sphere.…
There is a well studied notion of GIT-stability for coherent systems over curves, which depends on a real parameter $\alpha$. For generated coherent systems, there is a further notion of stability derived from Mumford's definition of linear…
We study Green functions for the pressure of stationary Stokes systems in a (possibly unbounded) domain $\Omega\subset \mathbb{R}^d$, where $d\ge 2$. We construct the Green function when coefficients are merely measurable in one direction…
At finite temperatures ($\geq 10^7$K), $^{76}$Se is abundant in the core of massive stars and electron capture on $^{76}$Se has a consequential role to play in the dynamics of core collapse. The present work may be classified into two main…
When noninteracting fermions are confined in a $D$-dimensional region of volume $\mathrm{O}(L^D)$ and subjected to a continuous (or piecewise continuous) potential $V$ which decays sufficiently fast with distance, in the thermodynamic…
The one-dimensional time-independent Green's function $G_0$ of a quantum simple harmonic oscillator system ($V_0(x)=m \omega^2 x^2/2$) can be obtained by solving the equation directly. It has a compact expression, which gives correct…
We study the motion of an overdamped particle connected to a thermal heat bath in the presence of an external periodic potential in one dimension. When we coarse-grain, i.e., bin the particle positions using bin sizes that are larger than…
In this paper, we derive global sharp heat kernel estimates for symmetric alpha-stable processes (or equivalently, for the fractional Laplacian with zero exterior condition) in two classes of unbounded C^{1,1} open sets in R^d:…