OPTIMAL ASYMPTOTIC BOUNDS FOR DESIGNS ON MANIFOLDS

We extend to the case of a d-dimensional compact connected oriented Riemannian manifold M the theorem of A. Bondarenko, D. Radchenko and M. Viazovska (Ann. of Math..2/ 178:2 (2013), 443-452) on the existence of L-designs consisting of N nodes for any N >= CMLd. For this, we need to prove a version of the Marcinkiewicz-Zygmund inequality for the gradient of diffusion polynomials.

Automated summary

The text discusses the extension of the theorem regarding L-designs by A. Bondarenko, D. Radchenko and M. Viazovska to d-dimensional compact connected oriented Riemannian manifolds. To prove this theorem, a version of the Marcinkiewicz-Zygmund inequality for the gradient of diffusion polynomials needs to be established.