Related papers: Carleson estimates for the Green function on domai…
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…
A simple integral representation is derived for the quasiclassical Green function of the Dirac equation in an arbitrary spherically-symmetric decreasing external field. The consideration is based on the use of the quasiclassical radial wave…
We characterize the Carleson measures for the Drury-Arveson Hardy space and other Hilbert spaces of analytic functions of several complex variables. This provides sharp estimates for Drury's generalization of Von Neumann's inequality. The…
In one-sided Chord-Arc Domains $\Omega$, we demonstrate that the $A_\infty$-absolute continuity of the elliptic measure with respect to the surface measure remains stable under $L^2$ Carleson perturbations. This stability holds provided…
An exact representation of the causal QED fermion Green's function, in an arbritrary external electromagnetic field, derived by Fried, Gabellini and McKellar, and which naturally allows for non-perturbative approximations, is here used to…
We develop an $e_g$ orbital, $t$-$J$-like model of a single charge doped into a two-dimensional plane with ferromagnetic spin order and alternating orbital order, and present its solution by Green's functions in the variational…
A general technique is developed for calculating functional determinants of second-order differential operators with Dirichlet, periodic, and antiperiodic boundary conditions. As an example, we give simple formulas for a harmonic oscillator…
We show that the acoustic Green`s function for a half-space impedance problem in arbitrary spatial dimension d can be written as a sum of two terms, each of which is the product of an exponential function with the eikonal in the argument…
Evaluation of the Bellman functions is a difficult task. The exact Bellman functions of the dyadic Carleson Embedding Theorem 1.1 and the dyadic maximal operators are obtained in [3] and [4]. Actually, the same Bellman functions also work…
We prove that bounded harmonic functions of anisotropic fractional Laplacians are H\"older continuous under mild regularity assumptions on the corresponding L\'evy measure. Under some stronger assumptions the Green function, Poisson kernel…
A theorem of Dorronsoro from the 1980s quantifies the fact that real-valued Sobolev functions on Euclidean spaces can be approximated by affine functions almost everywhere, and at all sufficiently small scales. We prove a variant of…
We construct a new functional for the single particle Green's function, which is a variant of the standard Baym Kadanoff functional. The stability of the stationary solutions to the new functional is directly related to aspects of the…
We discuss approximations of the Riemannian geometry near the horizon. If a D+1 dimensional manifold N has a bifurcate Killing horizon then we approximate N by a product of the two-dimensional Rindler space and a D-1 dimensional Riemannian…
The Green function has a complex dependence upon its underlying domain and differential operator. We briefly review Hadamard's formula for the first variation of the Green function due to a perturbation of the domain. We then take a…
Given a domain above a Lipschitz graph, we establish solvability results for strongly elliptic second-order systems in divergence-form, allowed to have lower-order (drift) terms, with $L^p$-boundary data for $p$ near $2$ (more precisely, in…
We give a generalisation of the character formula of Deligne--Lusztig representations from the finite field case to the truncated formal power series case. Motivated by this generalisation, we give a definition of Green functions for these…
Let $M$ be a pseudoconvex, oriented, bounded and closed CR submanifold of $\mathbb{C}^{n}$ of hypersurface type. We show that Sobolev estimates for the complex Green operator hold simultaneously for forms of symmetric bidegrees, that is,…
Acoustic room modes and the Green's function mode expansion are well-known for rectangular rooms with perfectly reflecting walls. First-order approximations also exist for nearly rigid boundaries; however, current analytical methods fail to…
A full characterization of the boundedness of Laplace--Carleson embeddings on $L^\infty$ is provided, in terms of the Carleson intensity of the respective measure and of a suitable weighted Berezin transform of the measure. Moreover,…
Flexible boundary condition methods couple an isolated defect to bulk through the bulk lattice Green's function. The inversion of the force-constant matrix for the lattice Green's function requires Fourier techniques to project out the…