Related papers: Functional determinants via Wronski construction o…
We derive an expression for the spectral determinant of a second-order elliptic differential operator $\mathcal{T}$ defined on the whole real line, in terms of the Wronskians of two particular solutions of the equation $\mathcal{T} u=0$.…
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…
In this paper, we analyze a second-order differential equation with a piecewise constant argument and reflection coupled to periodic boundary conditions. Our main contribution is the construction of the related Green's function and a…
We discuss various issues associated with the calculation of the reduced functional determinant of a special second order differential operator $\boldmath${F}$ =-d^2/d\tau^2+\ddot g/g$, $\ddot g\equiv d^2g/d\tau^2$, with a generic function…
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 construct an expression for the Green function of a differential operator satisfying nonlocal, homogeneous boundary conditions starting from the fundamental solution of the differential operator. This also provides the solution to the…
We model generalized harmonic functions on rings of differential operators and complex function spaces. The differential operators in the second Weyl-algebra that commute with rotations are described and leads to a natural notion for such…
In this article we propose the calculation of the unconditional Wiener measure functional integral with a term of the fourth order in the exponent by an alternative method as in the conventional perturbative approach. In contrast to the…
We study the zeta-function regularization of functional determinants of Laplace and Dirac-type operators in two-dimensional Euclidean $AdS_2$ space. More specifically, we consider the ratio of determinants between an operator in the…
We provide closed formulas for (unique) solutions of nonhomogeneous Dirichlet problems on balls involving any positive power $s>0$ of the Laplacian. We are able to prescribe values outside the domain and boundary data of different orders…
We present a holographic formula relating functional determinants: the fermion determinant in the one-loop effective action of bulk spinors in an asymptotically locally AdS background, and the determinant of the two-point function of the…
We construct Green's function for second order elliptic operators of the form $Lu=-\nabla \cdot (\mathbf{A} \nabla u + \boldsymbol{b} u)+ \boldsymbol c \cdot \nabla u+ du$ in a domain and obtain pointwise bounds, as well as Lorentz space…
In this paper, we establish a universal variational characterization of the non-martingale components associated with weakly differentiable Wiener functionals in the sense of Le\~ao, Ohashi and Simas. It is shown that any Dirichlet process…
In this paper we will deduce several properties of the Green's functions related to the Hill's equation coupled to various boundary value conditions. In particular, the idea is to study the Green's functions of the second order differential…
The functional determinant of a special second order quantum-mechanical operator is calculated with its zero mode gauged out by the method of the Faddeev-Popov gauge fixing procedure. This operator subject to periodic boundary conditions…
Simple and analytically tractable expressions for functional determinants are known to exist for many cases of interest. We extend the range of situations for which these hold to cover systems of self-adjoint operators of the…
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…
This paper investigates the Dirichlet problem for a non-divergence form elliptic operator $L$ in a bounded domain of $\mathbb{R}^d$. Under certain conditions on the coefficients of $L$, we first establish the existence of a unique Green's…
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…
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…