Related papers: Fourier decay, Green's kernel and Schottky groups
The thermal Euclidean Green functions for Photons propagating in the Rindler wedge are computed employing an Euclidean approach within any covariant Feynman-like gauge. This is done by generalizing a formula which holds in the Minkowskian…
Fourier decay of fractal measures on surfaces plays an important role in geometric measure theory and partial differential equations. In this paper, we study the quadratic surfaces of high co-dimensions. Unlike the case of co-dimension 1,…
Multiple scattering methods are widely used to reduce the computational complexity of acoustic or electromagnetic scattering problems when waves propagate through media containing many identical inclusions. Historically, this numerical…
In this paper, we build on the work of [T. Hughes, G. Sangalli, VARIATIONAL MULTISCALE ANALYSIS: THE FINE-SCALE GREENS' FUNCTION, PROJECTION, OPTIMIZATION, LOCALIZATION, AND STABILIZED METHODS, SIAM Journal of Numerical Analysis, 45(2),…
We consider the problem of calculating the Green's functions associated to a massive scalar field with modified dispersion relations. We analyze the case when dispersion is modified by higher derivative spatial operators acting on the field…
Given a sequence of regular planar domains converging in the sense of kernel, we prove that the corresponding Green's functions converge uniformly on the complex sphere, provided the limit domain is also regular, and the connectivity is…
With the help of Van der Corput lemmas, decay estimates are proven for Fourier transforms of mixed homogeneous hypersurface measures with densities that can be quite irregular. The primary results are local in nature, but can be extended to…
We consider the Cauchy problem for the Burgers hierarchy with general time dependent coefficients. The closed form for the Green's function of the corresponding linear equation of arbitrary order $N$ is shown to be a sum of generalised…
Summation formulas are obtained for products of associated Lagurre polynomials by means of the Green's function K for the Hamiltonian H = -{d^2\over dx^2} + x^2 + Ax^{-2}, A > 0. K is constructed by an application of a Mercer type theorem…
Several kernel-based methods for the numerical solution of fractional differential equations have been developed in the recent past; however, these techniques exclusively relied on the use of radial basis function approximations. In the…
In this paper, a new inversion model for 2D microwave imaging is introduced by means of a convenient rewriting of the usual Lippmann Schwinger integral scattering equation. Such model is derived by decomposing the Greens function and the…
Uniform $L^1$ and lower bounds are obtained for the Green's function on compact K\"ahler manifolds. Unlike in the classic theorem of Cheng-Li for Riemannian manifolds, the lower bounds do not depend directly on the Ricci curvature, but only…
Gross, Kohnen and Zagier proved an averaged version of the algebraicity conjecture for special values of higher Green's functions on modular curves. In this work, we study an analogous problem for special values of Green's functions on…
It is known that the equation $x'(t)=Ax(t)+f(t)$, where $A$ is a bounded linear operator, has a unique bounded solution $x$ for any bounded continuous free term~$f$ if and only if the spectrum of the coefficient $A$ does not intersect the…
A Green's function approach to the inclusive quasielastic ($e,e'$) scattering is presented. The components of the nuclear response are written in terms of the single-particle optical model Green's function. The explicit calculation of the…
In this note, we prove the uniform resolvent estimate of the discrete Schr\"odinger operator with dimension three. To do this, we show a Fourier decay of the surface measure on the Fermi surface.
Two-particle Green's functions and the vertex functions play a critical role in theoretical frameworks for describing strongly correlated electron systems. However, numerical calculations at two-particle level often suffer from large…
A simple and efficient formula is proposed for varying Abelian integrals (including their periods) under variation of the generators of the classical Schottky group representing a Riemann surface.
Single-particle resonances are crucial for exotic nuclei near and beyond the drip lines. Since the majority of nuclei are deformed, the interplay between deformation and orbital structure near threshold becomes very important and can lead…
In this paper, the Green's function and decomposition technique is proposed for solving the coupled Lane-Emden equations. This approach depends on constructing Green's function before establishing the recursive scheme for the series…