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A rational expansion of the Fermi density operator is proposed. This approach allows to calculate efficiently physical properties of fermionic systems at finite temperatures without solving an eigenvalue problem. Using N evaluations of the…
Green functions associated with higher-order differential operators typically lead to special-function expressions in curved or bounded geometries, obscuring analytic transparency. In this work we develop the sectorial Green function for…
For a family of weight functions invariant under a finite reflection group, the boundedness of a maximal function on the unit sphere is established and used to prove a multiplier theorem for the orthogonal expansions with respect to the…
In this paper we prove the basic facts for pluricomplex Green functions on manifolds. The main goal is to establish properties of complex manifolds that make them analogous to relatively compact or hyperconvex domains in Stein manifolds.…
We obtain simple formulas for the matrix elements of the resolvent operator (the Green's function) in any finite set of square integrable basis. These formulas are suitable for numerical computations whether the basis elements are…
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…
The theoretical investigation of charge (and spin) transport at nanometer length scales requires the use of advanced and powerful techniques able to deal with the dynamical properties of the relevant physical systems, to explicitly include…
Let $1\leq m\leq n$ be two fixed integers. Let $\Omega \Subset \mathbb C^n$ be a bounded $m$-hyperconvex domain and $\mathcal A \subset \Omega \times ]0,+ \infty[$ a finite set of weighted poles. We define and study properties of the…
The Green functions of the partial differential operators of even order acting on smooth sections of a vector bundle over a Riemannian manifold are investigated via the heat kernel methods. We study the resolvent of a special class of…
We obtain the Green's function $G$ for any flat rhombic torus $T$, always with numerical values of significant digits up to the fourth decimal place (noting that $G$ is unique for $|T|=1$ and $\int_TGdA=0$). This precision is guaranteed by…
We investigate the particle and kinetic-energy densities for $N$ non-interacting fermions confined in a local potential. Using Gutzwiller's semi-classical Green function, we describe the oscillating parts of the densities in terms of closed…
A geometry-based density functional theory is presented for mixtures of hard spheres, hard needles and hard platelets; both the needles and the platelets are taken to be of vanishing thickness. Geometrical weight functions that are…
We establish existence and pointwise estimates of fundamental solutions and Green's matrices for divergence form, second order strongly elliptic systems in a domain $\Omega \subseteq \mathbb{R}^n$, $n \geq 3$, under the assumption that…
Recent work on the quantization of Maxwell theory has used a non-covariant class of gauge-averaging functionals which include explicitly the effects of the extrinsic-curvature tensor of the boundary, or covariant gauges which, unlike the…
We derive equations of motion for higher order density response functions using the theory of thermodynamic Green's functions. We also derive expressions for the higher order generalized dielectric functions and polarization functions.…
In a previous paper, "Generalized Green functions and unipotent classes for finite reductive groups, I", we have determined certain unknown scalars involved in the algorithm of computing generalized Green functions in the case of SL_n. In…
The structure of diagonal singularities of Green functions of partial differential operators of even order acting on smooth sections of a vector bundle over a Riemannian man ifold is studied. A special class of operators formed by the…
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…
Recurrences for positive definite functions in terms of the space dimension have been used in several fields of applications. Such recurrences typically relate to properties of the system of special functions characterizing the geometry of…
In this note we establish the positivity of Green's functions for a class of elliptic differential operators on closed, Riemannian manifolds.