Related papers: On equivalent methods for functional determinants
A new method is presented for Fourier decomposition of the Helmholtz Green Function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of…
We study a discrete model of the Laplacian in $\mathbb{R}^2$ that preserves the geometric structure of the original continual object. This means that, speaking of a discrete model, we do not mean just the direct replacement of differential…
We develop a method for accurately calculating vacuum decay rates beyond the thin-wall regime in a pure scalar field theory at the one-loop level of the effective action. It accounts for radiative effects resulting from quantum corrections…
A consistent functional calculus approach to the spectral theorem for strongly commuting normal operators on Hilbert spaces is presented. In contrast to the common approaches using projection-valued measures or multiplication operators,…
We look at estimates for the Green's function of time-fractional evolution equations of the form $D^{\nu}_{0+*} u = Lu$, where $D^{\nu}_{0+*}$ is a Caputo-type time-fractional derivative, depending on a L\'evy kernel $\nu$ with variable…
Investigating the stability of nonlinear waves often leads to linear or nonlinear eigenvalue problems for differential operators on unbounded domains. In this paper we propose to detect and approximate the point spectra of such operators…
We present a characteristic initial value approach to calculating the Green function of the Regge-Wheeler and Zerilli equations. We combine well-known numerical methods with newly derived initial data to obtain a scheme which can in…
We introduce Neural Green's Function, a neural solution operator for linear partial differential equations (PDEs) whose differential operators admit eigendecompositions. Inspired by Green's functions, the solution operators of linear PDEs…
The calculation of both spinor and tensor Green's functions in four-dimensional conformally invariant field theories can be greatly simplified by six-dimensional methods. For this purpose, four-dimensional fields are constructed as…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
We prove that for an open domain $D \subset \mathbb{R}^d $ with $d \geq 2 $ , for every (measurable) uniformly elliptic tensor field $a$ and for almost every point $y \in D$ , there exists a unique Green's function centred in $ y $…
We study three types of generalized partial fractional operators. An extension of Green's theorem, by considering partial fractional derivatives with more general kernels, is proved. New results are obtained, even in the particular case…
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…
In this paper, we investigate the determinants involving some trigonometric functions. We establish a connection between these determinants and the special values of Dirichlet L-functions, thereby extending Guo's results to arbitrary…
We introduce a general approach to traces that we consider as linear continuous functionals on some function space where we focus on some special choices for that space. This leads to an integral calculus for the computation of the precise…
One of the landmarks of the modern theory of partial differential equations is the Malgrange- Ehrenpreis theorem that states that every non-zero linear partial differential operator with constant coefficients has a Green function (alias…
The g-function is a measure of degrees of freedom associated to a boundary of two-dimensional quantum field theories. In integrable theories, it can be computed exactly in a form of the Fredholm determinant, but it is often hard to evaluate…
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…
We study counter-terms of one- and two-point Green functions of some special operators in ${\cal N}=1$ SYM from their SUGRA duals from the consideration of AdS/CFT or gauge/gravity correspondence. We consider both the Maldacena-Nunez…
The conformal anomalies and functional determinants of the Branson--GJMS operators, P_{2k}, on the d-dimensional sphere are evaluated in explicit terms for any d and k such that k < d/2+1 (if d is even). The determinants are given in terms…