The group of diffeomorphisms of the circle: reproducing kernels and analogs of spherical functions

Yury A. Neretin

The group $Diff$ of diffeomorphisms of the circle is an infinite dimensional analog of the real semisimple Lie groups $U(p,q)$, $Sp(2n,R)$, $S{O}^{\ast }(2n)$; the space $\Xi$ of univalent f…