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arXiv · 1311.7343

Log concavity for matrix-valued functions and a matrix-valued Prékopa theorem

Hossein Raufi
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Abstract

We give two different definitions of what it means for a matrix-valued function to be log concave, guided by similar notions in complex differential geometry. After discussing a few simple examples, we proceed to develop some of the basic properties associated with these new concepts. Finally, we prove a matrix-valued Prékopa theorem using a weighted, vector-valued Paley-Wiener theorem, and positivity properties of direct image bundles.

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Hossein Raufi. 2013-11-28. Log concavity for matrix-valued functions and a matrix-valued Prékopa theorem. https://arxiv.org/abs/1311.7343

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