We consider the inverse problem of reconstructing the absorption and diffusion coefficients of an inhomogeneous highly scattering medium probed by diffuse light. Inversion formulas based on the Fourier-Laplace transform are used to establish the existence and uniqueness of solutions to this problem in planar, cylindrical, and spherical geometries.

In this paper we will study the existence of fundamental solutions for the explicit and implicit backward time dependent Schödinger equation, via discrete Fourier transform and its symbol for the Laplace operator. In both cases we will prove that the discrete fundamental solutions obtained converges to the continuous fundamental solution in the l1−norm sense.

We consider the inverse scattering problem for the radiative transport equation. We show that the linearized form of this problem can be formulated in terms of the inversion of a suitably defined Fourier-Laplace transform. This generalizes a previous result obtained within the diffusion approximation to the radiative transport equation.

Many stochastic processes are defined on special geometrical objects like spheres and cones. We describe how tools from harmonic analysis, i.e. Fourier analysis on groups, can be used to investigate probability density functions (pdfs) on groups and homogeneous spaces. We consider the special case of the Lorentz group SU(1,1) and the unit disk with its hyperbolic geometry, but the procedure can...

Several errors were introduced in the preparation of this article for publication. In the third sentence of the "Random walk with one turning angle" section of the Results, a symbol was removed from the definition of the Fourier-Laplace-transform. The correct definition can be found here:

We show that the Fourier-Laplace transform of an irreducible regular differential system on the Riemann sphere underlies, when one only considers the part at finite distance, a polarizable regular twistor D-module. The associated holomorphic bundle out of the origin is therefore equipped with a natural harmonic metric with a tame behaviour near the origin.

This article is devoted to the complete proof of the main theorem in the author’s paper of 2004 showing that the Fourier–Laplace transform of an irreducible regular differential system on the Riemann sphere underlies, at finite distance, a polarizable regular twistor Dmodule. 2000 Math. Subj. Class. Primary: 32S40; Secondary: 14C30, 34Mxx.

The topology of the weighted inductive limit of Fréchet spaces of entire functions in N variables which is obtained as the Fourier Laplace transform of the space of quasianalytic functionals on an open convex subset of R cannot be described by means of weighted supseminorms.

The basic three-dimensonal boundary-contact dynamic problems are considered for a piecewise-homogeneous isotropic elastic medium bounded by several closed surfaces. Using the Fourier method, the considered problems are proved to be solvable under much weaker restrictions on the initial data of the problems as compared with other methods. 1. Two well-known methods – the Laplace transform and the...