Spherical designs of harmonic index t

• Eiichi Bannai ^[1] ; Takayuki Okuda ^[2] ; Makoto Tagami ^[3]
  1. [1] Shanghai Jiao Tong University

     Shanghai Jiao Tong University

     China

     
  2. [2] Tohoku University

     Tohoku University

     Aoba-ku, Japón

     
  3. [3] Kyushu Institute of Technology

     Kyushu Institute of Technology

     Kokurakita Ku, Japón

     

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• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 195, Nº 1 (July 2015), 2015, págs. 1-18
• Idioma: inglés
• DOI: 10.1016/j.jat.2014.06.010
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• Resumen

  • Spherical tt-design is a finite subset on sphere such that, for any polynomial of degree at most tt, the average value of the integral on sphere can be replaced by the average value at the finite subset. It is well-known that an equivalent condition of spherical design is given in terms of harmonic polynomials. In this paper, we define a spherical design of harmonic index tt from the viewpoint of this equivalent condition, and we give its construction and a Fisher type lower bound on the cardinality. Also we investigate whether there is a spherical design of harmonic index attaining the bound.