Related papers: On equivalent methods for functional determinants
The Gelfand-Yaglom formula relates the regularized determinant of a differential operator to the solution of an initial value problem. Here we develop a generalized Gelfand-Yaglom formula for a Hamiltonian system with Lagrangian boundary…
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 consider Steklov eigenvalues on nearly spherical and nearly annular domains in $d$ dimensions. By using the Green-Beltrami identity for spherical harmonic functions, the derivatives of Steklov eigenvalues with respect to the domain…
The purpose of this work is to study spectral methods to approximate the eigenvalues of nonlocal integral operators. Indeed, even if the spatial domain is an interval, it is very challenging to obtain closed analytical expressions for the…
In this paper, we consider a discontinuous Dirac operator with eigenparameter dependent both boundary and two transmission conditions. We introduce a suitable Hilbert space formulation and get some properties of eigenvalues and…
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 calculate the four-point function of $1/2$-BPS determinant operators in $\mathcal{N}=4$ SYM at next-to-leading order at weak coupling. We use two complementary methods recently developed for a class of determinant three-point functions:…
During the past three decades, the advantageous concept of the Green's function has been extended from linear systems to nonlinear ones. At that, there exist a rigorous and an approximate extensions. The rigorous extension introduces the…
A new analytical operator method is discussed which solves linear ordinary differential equations with regular singularities. Solutions are obtained in analytic series form and also in Mellin-Barnes-type contour integral form. Exact series…
A new method for non-perturbative calculation of Green functions in quantum mechanics and quantum field theory is proposed. The method is based on an approximation of Schwinger-Dyson equation for the generating functional by exactly soluble…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
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.
Eigenvalues of the Breit equation, in which only the static Coulomb potential is considered, have been found. Over the past decades several authors have analyzed the Breit equation to obtain numerically or by approximation an estimation of…
The reduction algorithms for functional determinants of differential operators on spacetime manifolds of different topological types are presented, which were recently used for the calculation of the no-boundary wavefunction and the…
Semiclassical expansions for traces involving Greens functions have two contributions, one from the periodic or recurrent orbits of the classical system and one from the phase space volume, i.e. the paths of infinitesimal length.…
The core of this article is a general theorem with a large number of specializations. Given a manifold $N$ and a finite number of one-parameter groups of point transformations on $N$ with generators $Y, X_{(1)}, \cdots, X_{(d)} $, we…
A well-known theorem factors a scalar coefficient differential operator given a linearly independent set of functions in its kernel. The goal of this paper is to generalize this useful result to other types of operators. In place of the…
Convolution with Green's function of a differential operator appears in a lot of applications e.g. Lippmann-Schwinger integral equation. Algorithms for computing such are usually non-trivial and require non-uniform mesh. However, recently…
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…
{We explore a simple {\it geometric model} for functions between spaces of the same dimension (in infinite dimensions, we require that Jacobians be Fredholm operators of index zero). The model combines standard results in analysis and…