Related papers: Green function to the biharmonic equation on $n$-d…
Here we shall find the green's function of the difference equation of loop quantum cosmology. To illustrate how to use it, we shall obtain an iterative solution for closed model and evaluate its corresponding Bohmian trajectory.
We provide explicit representations of Green's functions for general linear fractional differential operators with {\it variable coefficients} and Riemann-Liouvilles derivatives. We assume that all their coefficients are continuous in $[0,…
If h is a ring-valued function on a simplicial complex G we can define two matrices L and g, where the matrix entries are the h energy of homoclinic intersections. We know that the sum over all h values on G is equal to the sum of the Green…
A method for the computation of scattering data and of the Green function for the one-dimensional Schr\"{o}dinger operator $H:=-\frac{d^2}{dx^2}+q(x)$ with a decaying potential is presented. It is based on representations for the Jost…
We study the Green function of the Poisson equation in two, three and four dimensions. The solution g of the equation nabla^2 g(x - x') = delta^(D)(x - x'), where x and x are D-dimensional position vectors, is customarily expanded into…
We discuss similarities and differences between Green Functions in Quantum Field Theory and polylogarithms. Both can be obtained as solutions of fixpoint equations which originate from an underlying Hopf algebra structure. Typically, the…
We construct the Green function for the mixed boundary value problem for the linear Stokes system in a two-dimensional Lipschitz domain.
The electromagnetic Green's function is a crucial ingredient for the theoretical study of modern photonic quantum devices, but is often difficult or even impossible to calculate directly. We present a numerically efficient framework for…
A numerical explicit method to evaluates transient solutions of linear partial differential non-homogeneous equation with constant coefficients is proposed.
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 the first part of this article we obtain an identity relating the radial spectrum of rotationally invariant geodesic balls and an isoperimetric quotient $\sum 1/\lambda_{i}^{\rm rad}=\int V(s)/S(s)ds$. We also obtain upper and lower…
Both the gauge-invariant fermion Green function and gauge-dependent conventional Green function in $ 2+1 $ dimensional QED are studied in the large $ N $ limit. In temporal gauge, the infra-red divergence of gauge-dependent Green function…
The motion of a small compact object in a curved background spacetime deviates from a geodesic due to the action of its own field, giving rise to a self-force. This self-force may be calculated by integrating the Green function for the wave…
Practical methods to compute dipole strengths for a three-body system by using a discretized continuum are analyzed. New techniques involving Green's function are developed, either by correcting the tail of the approximate wave function in…
The aim of this paper is to show certain properties of the Green's functions related to the Hill's equation coupled with different two point boundary value conditions. We will obtain the expression of the Green's function of Neumann,…
In this article we use linear algebra to improve the computational time for the obtaining of Green's functions of linear differential equations with reflection (DER). This is achieved by decomposing both the `reduced' equation (the ODE…
We consider a homogeneous space X=(X,d,m) of dimension $\nu \geq 1$ and a local regular Dirichlet form in L^{2}(X,m). We prove that if a Poincar\'{e} inequality holds on every pseudo-ball B(x,R) of X, with local characteristic constant…
We prove the existence and pointwise bounds of the Green functions for stationary Stokes systems with measurable coefficients in two dimensional domains. We also establish pointwise bounds of the derivatives of the Green functions under a…
We obtain various general conditions in terms of the balayage and Green's functions under which the sequence of points is the zero set for weighted spaces of holomorphic functions in a domain on the complex plane.
The square integrable basis set representation of the resolvent of the asymptotic three-body Coulomb wave operator in parabolic coordinates is obtained. The resulting six-dimensional Green's function matrix is expressed as a convolution…