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Optimal asymptotic
bounds for designs on manifolds
Bianca Gariboldi and Giacomo Gigante |
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Vol. 14 (2021), No. 6, 1701–1724
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Abstract |
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We extend to the case of a -dimensional compact connected oriented Riemannian manifold the theorem of A. Bondarenko, D. Radchenko and M. Viazovska (Ann. of Math. 178:2 (2013), 443–452) on the existence of -designs consisting of nodes for any . For this, we need to prove a version of the Marcinkiewicz–Zygmund inequality for the gradient of diffusion polynomials. |
Keywords
designs, Riemannian manifolds, Marcinkiewicz–Zygmund
inequalities
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Mathematical Subject Classification 2010
Primary: 41A55, 42C15
Secondary: 58J35
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Milestones
Received: 21 December 2018
Revised: 14 January 2020
Accepted: 19 March 2020
Published: 7 September 2021
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Authors |
| Bianca Gariboldi | |
| Dipartimento di Ingegneria
Gestionale, dell’Informazione e della Produzione Università degli Studi di Bergamo Dalmine Italy |
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| Giacomo Gigante | |
| Dipartimento di Ingegneria
Gestionale, dell’Informazione e della Produzione Università degli Studi di Bergamo Dalmine Italy |
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