Related papers: Green's Function For Linear Differential Operators…
We construct radial fundamental solutions for the differential form Laplacian on negatively curved symmetric spaces. At least one of these Green's functions also yields a Biot-Savart Opearator, i.e. a right inverse of the exterior…
An estimate of Green's function of the bounded solutions problem for the ordinary differential equation $x'(t)-Bx(t)=f(t)$ is proposed. It is assumed that the matrix coefficient $B$ is triangular. This estimate is a generalization of the…
Stieltjes boundary problems generalize the customary class of well-posed two-point boundary value problems in three independent directions, regarding the specification of the boundary conditions: (1) They allow more than two evaluation…
We derive formulas for the matrix elements of the lattice Green function for the discrete Poisson equation on an infinite square lattice. The partial difference equation for the matrix elements is solved by reducing it to a series of first…
Explicit solutions of differential equations of complex fractional orders with respect to functions and with continuous variable coefficients are established. The representations of solutions are given in terms of some convergent infinite…
In this short note we review some facts about elliptic differential operators on Riemannian manifolds.
An iterative formula for the Green polynomial is given using the vertex operator realization of the Hall-Littlewood function. Based on this, (1) a general combinatorial formula of the Green polynomial is given; (2) several compact formulas…
We show that Green functions of second-order differential operators with singular or unbounded coefficients can have an anomalous behaviour in comparison to the well-known properties of Green functions of operators with bounded…
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 explore the connections between Green's functions for certain differential equations, covariance functions for Gaussian processes, and the smoothing splines problem. Conventionally, the smoothing spline problem is considered in a setting…
A latent force model is a Gaussian process with a covariance function inspired by a differential operator. Such covariance function is obtained by performing convolution integrals between Green's functions associated to the differential…
We consider a general one-particle Hamiltonian H = - \Delta_r + u(r) defined in a d-dimensional domain. The object of interest is the time-independent Green function G_z(r,r') = < r | (z-H)^{-1} | r' >. Recently, in one dimension (1D), the…
Discrete Green's functions are the inverses or pseudo-inverses of combinatorial Laplacians. We present compact formulas for discrete Green's functions, in terms of the eigensystems of corresponding Laplacians, for products of regular graphs…
We develop a causal optimization method that ensures causality in numerical calculations of Green's functions in interacting electron systems. Our method removes noncausality of numerical data by finding causal functions closest to the…
The fundamental solution (Green's function) of a first order matrix ordinary differential equation arising in a Landau-type problem is calculated by two methods. The coincidence of the two representations results in the integral formula for…
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…
A method of generating differential operators is used to solve the spectral problem for a generalisation of the Sylvester-Kac matrix. As a by-product, we find a linear differential operator with polynomial coefficients of the first order…
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 investigate a first boundary value problem for a second-order partial differential equation involving the Prabhakar fractional derivative in time. Using structural properties of the Prabhakar kernel and generalized Mittag-Leffler…
If a linear differential operator with rational function coefficients is reducible, its factors may have coefficients with numerators and denominatorsof very high degree. When the base field is $\mathbb C$, we give a completely explicit…