We construct the Hadamard Green’s function by using the eigenfunction, which are obtained by solving the wave equation for the massless conformal scalar field on the Sn−1 of a n-dimensional closed, static universe. We also consider the half space case with both the Dirichlet and the Neumann boundary conditions. Solving of eigenfunction and eigenvalues of the corresponding field equation is inte...

Recent experimental results have shown that the presence of a steady current can significantly reduce the energy of transmitted waves. In this paper, a theory is developed to study the wave scattering by single or double vertical slotted barriers in the presence of a weak uniform current. The quasi-linear theory is based on an eigenfunction expansion method. Comparisons with existing experiment...

The square root constant elasticity of variance (CEV) process has been paid little attention in previous research on valuation of barrier options. In this paper we derive analytical option pricing formulae of up-and-out options with this process using the eigenfunction expansion technique. We develop an efficient algorithm to compute the eigenvalues where the basis functions in the formulae are...

Thermoelastic expansion due to frictional heating causes significant changes in contact pressure and temperature in energy dissipation systems uch as brakes and clutches. Finite element analysis of such systems tends to be extremely computer-intensive. We here present an alternative mplementation of the transient problem, based on the expression of the temperature and stress fields as modal exp...

A class of singular integral operators, encompassing two physically relevant cases arising in perturbative QCD and in classical fluid dynamics, is presented and analyzed. It is shown that three special values of the parameters allow for an exact eigenfunction expansion; these can be associated to Riemannian symmetric spaces of rank one with positive, negative or vanishing curvature. For all oth...

In this article, by extending the method of [AC] we prove a sharp estimate on the expansion modulus of the gradient of the logarithm of the parabolic kernel to the Schördinger operator with convex potential on a bounded convex domain. The result improves an earlier work of Brascamp-Lieb which asserts the log-concavity of the parabolic kernel. We also give an alternate proof to a corresponding e...