Related papers: Green's Function For Linear Differential Operators…
Lusztig's algorithm of computing generalized Green functions of reductive groups involves an ambiguity of certain scalars. In this paper, for reductive groups of classical type with arbitrary characteristic, we determine those scalars…
We establish quantitative Green's function estimates for a class of quasi-periodic (QP) operators on $\mathbb{Z}^d$ with certain slowly decaying long-range hopping and analytic cosine type potentials. As applications, we prove the…
The Green's function, serving as a kernel function that delineates the interaction relationships of physical quantities within a field, holds significant research implications across various disciplines. It forms the foundational basis for…
The Laplace transform method for solving of a wide class of initial value problems for fractional differential equations is introduced. The method is based on the Laplace transform of the Mittag-Leffler function in two parameters. To extend…
We derive formulas for the matrix elements of the two dimensional square lattice Green function along the diagonal, and along the coordinate axes. We also give an asymptotic formula for the diagonal elements.
We show how to get explicit induction formulae for finite group representations, and more generally for rational Green functors, by summing a divergent series over Dwyer's subgroup and centralizer decomposition spaces. This results in…
We prove the existence of the Green's function for radial SLE(k) for k<8. Unlike the chordal case where an explicit formula for the Green's function is known for all values of k<8, we give an explicit formula only for k=4. For other values…
Dyadic Green's function is an important tool of computational photonics, giving deeper insights into light-matter interaction. We present an operator approach to the derivation of the dyadic Green's function of a generic anisotropic…
Recently, general point interactions in one dimension has been used to model a large number of different phenomena in quantum mechanics. Such potentials, however, requires some sort of regularization to lead to meaningful results. The usual…
In one variable, there exists a satisfactory classification of commutative rings of differential operators. In several variables, even the simplest generalizations seem to be unknown and in this report we give examples and pose questions…
In this paper, a regression algorithm based on Green's function theory is proposed and implemented. We first survey Green's function for the Dirichlet boundary value problem of 2nd order linear ordinary differential equation, which is a…
Green's functions in Physics have proven to be a valuable tool for understanding fundamental concepts in different branches, such as electrodynamics, solid-state and many -body problems. In quantum mechanics advanced courses, Green's…
Using the Gegenbauer polynomials and the zonal harmonics functions we give some representation formula of the Green function in the annulus. We apply this result to prove some uniqueness results for some nonlinear elliptic problems.
Gauge invariant quark two-point Green's functions defined with path-ordered gluon field phase factors along skew-polygonal lines joining the quark to the antiquark are considered. Functional relations between Green's functions with…
In this paper, we define the Green function for the Dirac operator under two local boundary conditions: the condition associated with a chirality operator (also called the chiral bag boundary condition) and the $\MIT$ bag boundary…
We present the Composite Operator Method (COM) as a modern approach to the study of strongly correlated electronic systems, based on the equation of motion and Green's function method. COM uses propagators of composite operators as building…
In this study, a recursive solution technique in conjunction with generalized integrating factors is presented and applied to address first and second order linear differential equations. This approach demonstrates practical utility in…
We are using the finite-gap approach for the construction of the Schr\"{o}dinger operator discretization on a quad graph. The latter is represented by a two-dimensional integer sublattice in a $d$-dimensional space. The Green's function of…
This paper introduces a probability density estimator based on Green's function identities. A density model is constructed under the sole assumption that the probability density is differentiable. The method is implemented as a binary…
We present a method for calculating the results of operation of differential operators operating on components of vector in generalized coordinates not restricted to orthogonal one. For this we use the relationships between covariant,…