Related papers: Green's Function For Linear Differential Operators…
A linear algebraic method named the shifted conjugate-orthogonal-conjugate-gradient method is introduced for large-scale electronic structure calculation. The method gives an iterative solver algorithm of the Green's function and the…
A method is given to obtain the Green's function for the Poisson equation in any arbitrary integer dimension under periodic boundary conditions. We obtain recursion relations which relate the solution in d-dimensional space to that in…
We derive a closed-form expression for the Green function of linear evolution equations with the Dirichlet boundary condition for an arbitrary region, based on the singular perturbation approach to boundary problems.
This paper is devoted to prove the existence of positive solutions of a second order differential equation with a nonhomogeneous Dirichlet conditions given by a parameter dependence integral. The studied problem is a nonlocal perturbation…
We define the concept of completely regular ordinary differential operators and give various criteria for operators to belong to this class. We give also criteria for Birkhof regularity of ordinary differential operators in terms of the…
If P is a differential operator with constant coefficients, an identity is derived to calculate the action of exp(P) on the product of two functions. In many-body theory, P describes the interaction Hamiltonian and the identity yields a…
Motivated by applications to stochastic programming, we introduce and study the expected-integral functionals, which are mappings given in an integral form depending on two variables, the first a finite dimensional decision vector and the…
In this paper, we give the explicit expressions of high-order Green operators on the disk and the polydisc, and hence the kernel functions of high-order Green operators are also presented. As applications, we present the explicit integral…
We use the newly introduced conformable fractional derivative, which is different from the Caputo and Riemann-Liouville fractional derivatives, to reformulate several common boundary value problems, including those with conjugate,…
The Green's function of the discrete Sch\"odinger operator on a finite graph is considered. This setting reproduces Laplacian and signless Laplacian by adjusting appropriate potentials. We show two ways of the expression for the Green's…
This paper is concerned with the study of Green's functions for one dimensional diffusions with constant diffusion coefficient and linear time inhomogeneous drift. It is well know that the whole line Green's function is given by a Gaussian.…
The heat operator with a pure soliton potential is considered and its Green's function, depending on a complex spectral parameter k, is derived. Its boundedness properties in all variables and its singularities in the spectral parameter k…
Computing functional determinants of differential operators is central to any field-theoretical calculation relying on a saddle-point expansion. A variety of approaches is available for the computation that avoid having to know the…
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…
Just as knowing some roots of a polynomial allows one to factor it, a well-known result provides a factorization of any scalar differential operator given a set of linearly independent functions in its kernel. This note provides a…
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 and the domain has $C^{1,1}$ boundary. We also obtain pointwise bounds for…
Based on results of Digne-Michel-Lehrer (2003) we give two formulae for two-variable Green functions attached to Lusztig induction in a finite reductive group. We present applications to explicit computation of these Green functions, to…
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…
We systematically introduce the idea of applying differential operator method to find a particular solution of an ordinary nonhomogeneous linear differential equation with constant coefficients when the nonhomogeneous term is a polynomial…
Parameters of differential equations are essential to characterize intrinsic behaviors of dynamic systems. Numerous methods for estimating parameters in dynamic systems are computationally and/or statistically inadequate, especially for…