Functional Analysis and Applications Seminar 

24/02/2012, 15:00 — 16:00 — Room P3.10, Mathematics Building
Stefan Samko, Universidade do Algarve e CEAF, IST

Spherical fractional integrals and their application to a problem

We first present some facts from the Spherical Harmonic Analysis, related to decompositions of functions into series of spherical harmonics and spherical convolution operators invariant with respect to rotations. Then we use some properties of spherical convolution operators to solve an integral equation over semishere in the n-dimensional Euclidean space which arises in a certain problem of aerodynamics. In this problem there is considered a rarefied medium of non-interacting point masses moving at unit velocity in all directions. Given the density of the velocity distribution, one easily calculates the pressure created by the medium in any direction. We consider the inverse problem: given the pressure distribution, determine the density. This leads to the problem of solving the above mentioned integral equation. In the "application part" the talk is based on a joint paper with Alexander Plakhov (Universidade de Aveiro).