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April, 2012 Loewner matrices of matrix convex and monotone functions
Fumio HIAI, Takashi SANO
J. Math. Soc. Japan 64(2): 343-364 (April, 2012). DOI: 10.2969/jmsj/06420343

Abstract

The matrix convexity and the matrix monotony of a real C1 function f on (0,∞) are characterized in terms of the conditional negative or positive definiteness of the Loewner matrices associated with f, tf(t), and t2f(t). Similar characterizations are also obtained for matrix monotone functions on a finite interval (a,b).

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Fumio HIAI. Takashi SANO. "Loewner matrices of matrix convex and monotone functions." J. Math. Soc. Japan 64 (2) 343 - 364, April, 2012. https://doi.org/10.2969/jmsj/06420343

Information

Published: April, 2012
First available in Project Euclid: 26 April 2012

zbMATH: 1261.15026
MathSciNet: MR2916071
Digital Object Identifier: 10.2969/jmsj/06420343

Subjects:
Primary: 15A45
Secondary: 42A82, 47A63

Rights: Copyright © 2012 Mathematical Society of Japan

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Vol.64 • No. 2 • April, 2012
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