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January 2003 Spherical t-designs and the Bernstein Theorem
Shigeto Nishimura
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SUT J. Math. 39(1): 1-14 (January 2003). DOI: 10.55937/sut/1059540776


In this paper we study the construction problem of spherical t-designs as a generalization of the Chebyshev problem of Gauss type quadrature formula. It is known that spherical t-designs can be constructed if we can construct interval t-designs for the weight function (1x)d22. We shall show the exsitence and non-existence theorems of some interval t-desings.


It is a pleasure to express my sincere gratitude to the referee for his valuable comments.


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Shigeto Nishimura. "Spherical t-designs and the Bernstein Theorem." SUT J. Math. 39 (1) 1 - 14, January 2003.


Received: 23 October 2001; Revised: 19 June 2002; Published: January 2003
First available in Project Euclid: 18 June 2022

Digital Object Identifier: 10.55937/sut/1059540776

Primary: 05B30 , 65D30

Keywords: Gauss type quadrature formula , spherical designs , the Gegenbauer polynomials

Rights: Copyright © 2003 Tokyo University of Science

Vol.39 • No. 1 • January 2003
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