Abstract In this paper we investigate the following questions. Let $$\mu , \nu $$ μ , ν be two regular Borel measures of finite total variation. When do have a constant C satisfying $$\begin{aligned} \int f d\nu \le d\mu \end{aligned}$$ <mm...

We consider interpolation methods defined by positive definite functions on a compact group. Estimates for the smallest and largest eigenvalue of the interpolation matrix in terms of the localization of the positive definite function on G are presented and we provide a method to get positive definite functions explicitly on compact semisimple Lie groups. Finally we apply our results to construc...