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Exact point-distributions over the complex sphere

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Abstract

We study point-distributions over the surface of the unit sphere in unitary space that generate quadrature rules which are exact for spherical polynomials up to a certain bi-degree. In this first stage, we explore several different characterizations for this type of point sets using standard tools such as, positive definiteness, reproducing kernel techniques, linearization formulas, etc. We find bounds on the cardinality of a point-distribution, without discussing the deeper question regarding best bounds. We include examples, construction methods and explain, via isometric embeddings from real to complex spheres, the proper connections with the so-called spherical designs.

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Authors and Affiliations

  1. Departamento de Matemática, ICMC-USP - São Carlos, Caixa Postal 668, São Carlos, SP, 13560-970, Brazil

    V. A. Menegatto & A. P. Peron

  2. Universidade Federal de Itajubá, ICE-DMC, Caixa Postal 50, Itajubá, MG, 37500-903, Brazil

    C. P. Oliveira

Authors
  1. V. A. Menegatto
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  2. C. P. Oliveira
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  3. A. P. Peron
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Correspondence to V. A. Menegatto.

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Communicated by Dr. W. H. Haemers.

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Menegatto, V.A., Oliveira, C.P. & Peron, A.P. Exact point-distributions over the complex sphere. Des. Codes Cryptogr. 60, 203–223 (2011). https://doi.org/10.1007/s10623-010-9425-5

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  • DOI: https://doi.org/10.1007/s10623-010-9425-5

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