Spherical t-designs and the Bernstein Theorem

Shigeto Nishimura

doi:10.55937/sut/1059540776

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Home > Journals > SUT J. Math. > Volume 39 > Issue 1 > Article

January 2003 Spherical

t

-designs and the Bernstein Theorem

Shigeto Nishimura

Author Affiliations +

Shigeto Nishimura¹
¹Department of Systems and Control Engineering, Faculty of Engineering, Hosei University Kajino-cho 3-7-2, Koganei-shi, Tokyo, 184-8584, Japan

SUT J. Math. 39(1): 1-14 (January 2003). DOI: 10.55937/sut/1059540776

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Abstract

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 ${(1 - x)^{{{d - 2} \over 2}}}$ . We shall show the exsitence and non-existence theorems of some interval $t$ -desings.

Acknowledgment

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. https://doi.org/10.55937/sut/1059540776