Related papers: Remarks on computing Green functions
We consider a fractional Laplace equation and we give a self-contained elementary exposition of the representation formula for the Green function on the ball. In this exposition, only elementary calculus techniques will be used, in…
We prove explicit bounds on canonical Green functions of Riemann surfaces obtained as compactifications of quotients of the upper half-plane by Fuchsian groups.
We propose a general method to obtain the scalar worldline Green function on an arbitrary 1D topological space, with which the first-quantized method of evaluating 1-loop Feynman diagrams can be generalized to calculate arbitrary ones. The…
An algorithm for computing power conjugate presentations for finite soluble quotients of predetermined structure of finitely presented groups is described. Practical aspects of an implementation are discussed.
We construct Green functions of conormal derivative problems for the stationary Stokes system with measurable coefficients in a two dimensional Reifenberg flat domain.
Green functions play an important role in conformal geometry. In this paper, we explain how to compute explicitly the logarithmic singularities of the Green functions of the conformal powers of the Laplacian. These operators include the…
We investigate two specific Green functions in the framework of chiral perturbation theory. We show that, using analyticity and unitarity, their leading logarithmic singularities can be evaluated in the chiral limit to any desired order in…
The single-particle Green's function (GF) of mesoscopic structures plays a central role in mesoscopic quantum transport. The recursive GF technique is a standard tool to compute this quantity numerically, but it lacks physical transparency…
We propose a new procedure by using the recursive Green's functions which remove all the repetition terms from the time-independent perturbation series for finite-level quantum systems. These Green's functions are introduced as a…
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…
Green's function provides an inherent connection between theoretical analysis and numerical methods for elliptic partial differential equations, and general absence of its closed-form expression necessitates surrogate modeling to guide the…
In this paper, we obtain a unified characterization of uniformly rectifiable sets of {\it any codimension} in terms of a Carleson estimate on the second derivatives of the Green function. When restricted to domains with boundaries of…
In this work we present a three step procedure for generating a closed form expression of the Green's function on both closed and open finite quantum graphs with general self-adjoint matching conditions. We first generalize and simplify the…
The properties of the gauge invariant two-point quark Green's function are studied in the large-Nc limit of two-dimensional QCD. The analysis is done by means of an exact integrodifferential equation. The Green's function is found infrared…
The two-time Green function method in quantum electrodynamics of high-Z few-electron atoms is described in detail. This method provides a simple procedure for deriving formulas for the energy shift of a single level and for the energies and…
We propose a general framework for computing Retarded Green's Functions (RGFs) on quantum computers by recasting their evaluation as a problem of circuit differentiation. Our proposal is based on real-time evolution and specifically…
A new interpretation of zeta functions is given for F1-schemes which do not satisfy Soul\'e's condition. Functional equations for reductive groups are computed and a new definition of zeta functions attached to more general counting…
Green's relations on the deformed finite inverse symmetric semigroup $\mathcal{IS}_n$ and the deformed finite symmetric semigroup $\mathcal{T}_n$ are described.
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. We show that the Green's function is BMO in the domain and establish…
We prove a Green--Tao theorem for multiplicative functions.