Notes on Sobolev spaces on compact classical groups and Stein--Sahi representations

Yuri A. Neretin

We discuss kernels on complact classical groups $G=\U(n)$, $\OO(2n)$, $\Sp(n)$ defined by the formula $K(z,u)=|\det (1-z{u}^{\ast }){|}^s$. We obtain the explicit Plancherel formula for these…