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 ≥ C_M L^d. For this, we need to prove a version of the Marcinkiewicz–Zygmund inequality for the gradient of diffusion polynomials.
(2021). Optimal asymptotic bounds for designs on manifolds [journal article - articolo]. In ANALYSIS & PDE. Retrieved from http://hdl.handle.net/10446/190334
Optimal asymptotic bounds for designs on manifolds
Gariboldi, Bianca;Gigante, Giacomo
2021-01-01
Abstract
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 ≥ C_M L^d. For this, we need to prove a version of the Marcinkiewicz–Zygmund inequality for the gradient of diffusion polynomials.File allegato/i alla scheda:
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