Masatake Hirao

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The aim of this paper is to develop the existence and nonexistence problem of a cubature formula of degree 4k+1 for a spherically symmetric integral which attains the Möller lower bound. For this purpose we bring together the theory of Euclidean design in combinatorics and that of reproducing kernels in numerical analysis. We show that if there exists a(More)
Acknowledgements I would like to express my deepest appreciation to my adviser Professor Hiroyuki Mat-sumoto. He has supervised my study for six and a half years and his continuous encouragement , patience, and excellent guidance had led me to successfully complete this thesis. I am especially indebted to Professor Eiichi Bannai, Professor Etsuko Bannai for(More)
Abstract. In this paper we consider the existence problem of cubature formulas of degree 4k+1 for spherically symmetric integrals for which the equality holds in the Möller lower bound. We prove that for sufficiently large dimensional minimal formulas, any two distinct points on some concentric sphere have inner products all of which are rational numbers.(More)
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