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On Group Induced Orderings, Monotone Functions, and Convolution Theorems
Morris L. Eaton
Lecture Notes-Monograph Series
Vol. 5, Inequalities in Statistics and Probability (1984), pp. 13-25
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/4355478
Page Count: 13
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Orderings defined by compact groups of linear transformations acting on vector spaces are studied. In some cases, these orderings induce orderings on convex cones similar to those defined by reflection groups. In these cases the monotone functions can be conveniently characterized. Convolution theorems for monotone functions are discussed.
Lecture Notes-Monograph Series © 1984 Institute of Mathematical Statistics