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arXiv · 1812.05482

A panorama of positivity

Alexander Belton·Dominique Guillot·Apoorva Khare·Mihai Putinar
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Abstract

This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or mass distributions). We put emphasis on entrywise operations which preserve positivity, in a variety of guises. Techniques from harmonic analysis, function theory, operator theory, statistics, combinatorics, and group representations are invoked. Some partially forgotten classical roots in metric geometry and distance transforms are presented with comments and full bibliographical references. Modern applications to high-dimensional covariance estimation and regularization are included.

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Alexander Belton, Dominique Guillot, Apoorva Khare, Mihai Putinar. 2018-12-13. A panorama of positivity. https://doi.org/10.1007/978-3-030-14640-5_5

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