Stefan Samko
(Universidade do Algarve e CEAF, IST)
" Spherical fractional integrals and
their application to a problem of aerodynamics "
Abstract. 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).
