The notion of a Green function is fundamental in the study of linear PDEs.
It models the displacement under a point charge of a membrane
(for the laplacian) and that of a plate (for the bilaplacian).
The notion of reproducing kernels of Hilbert spaces of functions was
developed by Moore and Aronszajn, and in the context of the (Bergman) space
of square area integrable analytic functions we get the Bergman
kernel, while in the context of the (harmonic Bergman) space of square
area integrable harmonic functions we get the harmonic Bergman
kernel. As it turns out, the Green function for the laplacian is
connected with the Bergman kernel, while the Green function for the
bilaplacian is connected with the harmonic Bergman kernel.
Garabedian introduced weighted variants of of the above Green functions,
and showed the connection with weighted Bergman and weighted harmonic Bergman
kernels. It is intended that the students should understand these notions
and connections, as well as make explicit calculations of Green functions etc
in some weighted cases.
![[KTHs logo]](start_logo.gif){kind=logo}