Abstract

Voronoï's theorem characterizes local maxima of the Hermite invariant m / det1/n defined on the open cone of positive definite n by n symmetric matrices, where m denotes the arithmetical minimum function. In this paper, we extend Voronoï's theorem to functions of the form m / φ when φ is a type one function. Moreover, we study the Hermite like constant defined from m / φ

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Kazuomi Sawatani

Dept. of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0001, Japan

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Suggested citation

K. Sawatani, T. Watanabe. “Type One Functions and Voronoï's Theorem.” Journal of Convex Analysis 18 (2011), No. 2, 341–351. https://doi.org/10.68381/jca18018

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Published by Heldermann Verlag, 2011. Rights now held by Banach Press.