
Journal of Convex Analysis 18 (2011), No. 2, 341351 Copyright Heldermann Verlag 2011 Type One Functions and Voronoļ's Theorem Kazuomi Sawatani Dept. of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 5600001, Japan Takao Watanabe Dept. of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 5600001, Japan twatanabe@math.sci.osakau.ac.jp Voronoļ's theorem characterizes local maxima of the Hermite invariant m / det^{1/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. [ Fulltextpdf (142 KB)] for subscribers only. 