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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
Stable URL: http://www.jstor.org/stable/4355478
Page Count: 13
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On Group Induced Orderings, Monotone Functions, and Convolution Theorems
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Abstract

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.

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