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Abstract: Using the theory of determinantal point processes we give upper bounds for the Green and Riesz energies for the rotation group SO(3), with Riesz parameter up to 3. The Green function is computed explicitly, and a lower bound for the Green energy is established, enabling comparison of uniform point constructions on SO(3). The variance of rotation matrices sampled by a certain determinantal point process is estimated, and formulas for the L2-norm of Gegenbauer polynomials with index 2 are deduced, which might be of independent interest
Fuente: Constructive Approximation, 2020, 52(2), 283 - 311
Publisher: Springer-Verl. New York.
Publication date: 01/10/2020
No. of pages: 29
Publication type: Article
DOI: 10.1007/s00365-020-09506-1
ISSN: 0176-4276,1432-0940
Spanish project: MTM2017-83816-P
Publication Url: https://doi.org/10.1007/s00365-020-09506-1
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CARLOS BELTRAN ALVAREZ
FERIZOVC, DAMIR
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