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

2013/11/28 by Hossein Raufi, Raufi, Hossein · 3 citations
Mathematics · #Geometry and complex manifolds #Holomorphic and Operator Theory #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1311.7343

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.

Cited by

• The openness conjecture and complex Brunn-Minkowski inequalities
• Curvature positivity of invariant direct images of Hermitian vector bundles
• Variation of Bergman kernels of pseudoconvex domains

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