• Corpus ID: 119167737

Inner products for Convex Bodies

@article{Bryant2018InnerPF,
  title={Inner products for Convex Bodies},
  author={David Bryant and Petru A. Cioica-Licht and Lisa Orloff Clark and Rachael Young},
  journal={arXiv: Metric Geometry},
  year={2018}
}
We define a set inner product to be a function on pairs of convex bodies which is symmetric, Minkowski linear in each dimension, positive definite, and satisfies the natural analogue of the Cauchy-Schwartz inequality (which is not implied by the other conditions). We show that any set inner product can be embedded into an inner product space on the associated support functions, thereby extending fundamental results of Hormander and Radstrom. The set inner product provides a geometry on the… 

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