Journal of Convex Analysis 18 (2011), No. 2, 341--351
Copyright Heldermann Verlag 2011
Type One Functions and Voronoļ's Theorem
Kazuomi Sawatani
Dept. of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0001, Japan
Takao Watanabe
Dept. of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0001, Japan
twatanabe@math.sci.osaka-u.ac.jp
Voronoļ'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 Voronoļ'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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