Related papers: An explicit Koppelman formula for $dd^c$ and Green…

Arakelov-Green functions defined on metrized graphs have important role in relating arithmetical problems on algebraic curves into graph theoretical problems. In this paper, we clarify the combinatorial interpretation of certain…

In this paper the fixed-energy amplitude (Green's function) of the relativistic Coulomb system is solved by Duru-Kleinert (DK) method. In the course of the calculations we observe an equivalence between the relativistic Coulomb system and a…

We present a simple recipe to construct the Green's function associated with a Hamiltonian of the form H=H_0+V, where H_0 is a Hamiltonian for which the associated Green's function is known and V is a delta-function potential. We apply this…

We develop the study of some spaces of currents of bidegree (p,p). As an application we construct the equilibrium measure for a large class of birational maps of P^k as intersection of Green currents. We show that these currents are…

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…

Let $X$ be an analytic space of pure dimension. We introduce a formalism to generate intrinsic weighted Koppelman formulas on $X$ that provide solutions to the $\dbar$-equation. We prove that if $\phi$ is a smooth $(0,q+1)$-form on a Stein…

Time-dependent quantum mechanics provides an intuitive picture of particle propagation in external fields. Semiclassical methods link the classical trajectories of particles with their quantum mechanical propagation. Many analytical results…

We construct an integral representation for the momentum space Green's function for a Neutron in interaction with a straight current carrying wire.

Using a new representation for the quasiclassical Green function of the Dirac equation in a Coulomb field, analytical expressions for the high-energy small-angle Delbr\"uck scattering amplitudes are obtained exactly in the parameter…

We provide quantitative inductive estimates for Green's functions of matrices with (sub)expoentially decaying off diagonal entries in higher dimensions. Together with Cartan's estimates and discrepancy estimates, we establish explicit…

In this study, we address the challenge of obtaining a Green's function operator for linear partial differential equations (PDEs). The Green's function is well-sought after due to its ability to directly map inputs to solutions, bypassing…

We construct Green's function for second order elliptic operators of the form $Lu=-\nabla \cdot (\mathbf{A} \nabla u + \boldsymbol{b} u)+ \boldsymbol c \cdot \nabla u+ du$ in a domain and obtain pointwise bounds, as well as Lorentz space…

The emphasis of this course is on pluripotential methods in complex dynamics in higher dimension. They are based on the compactness properties of plurisubharmonic functions and on the theory of positive closed currents. Applications of…

This article is devoted to deduce the expression of the Green's function related to a general constant coefficients fractional difference equation coupled to Dirichlet conditions. In this case, due to the points where some of the fractional…

We construct the Green function for second order elliptic equations in non-divergence form when the mean oscillations of the coefficients satisfy the Dini condition and the domain has $C^{1,1}$ boundary. We also obtain pointwise bounds for…

We compute the 2-point (equal-time) electronic Green function in a Tomonaga-Luttinger system with long-range electron-electron interactions. We obtain an analytical expression for a "super long-range" potential of the form…

A Green's function approach is presented for the D-dimensional inverse square potential in quantum mechanics. This approach is implemented by the introduction of hyperspherical coordinates and the use of a real-space regulator in the…

We present a new method for the existence and pointwise estimates of a Green's function of non-divergence form elliptic operator with Dini mean oscillation coefficients. We also present a sharp comparison with the corresponding Green's…

We find good dynamical compactifications for arbitrary polynomial mappings of C^2 and use them to show that the degree growth sequence satisfies a linear integral recursion formula. For maps of low topological degree we prove that the Green…

For meromorphic maps of complex manifolds, ergodic theory and pluripotential theory are closely related. In nice enough situations, dynamically defined Green's functions give rise to invariant currents which intersect to yield measures of…