Cubature formulas and Sobolev inequalities

Eli Putterman

We study a problem in the theory of cubature formulas on the sphere: given $\theta \in (0,1)$, determine the infimum of $\Vert \nu {\Vert }_{\theta }={\sum }_{i=1}^n{\nu }_i^{\theta }$ over cubature formulas $\nu$ of str…