A panorama of positivity. I: dimension free

Belton, Alexander and Guillot, Dominique and Khare, Apoorva and Putinar, Mihai (2019) A panorama of positivity. I: dimension free. In: Analysis of Operators on Function Spaces : The Serguei Shimorin Memorial Volume. Trends in Mathematics . Birkhauser, Cham, pp. 117-165. ISBN 9783030146399

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This survey contains a selection of topics unified by the concept of positive semidefiniteness (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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22 Jun 2019 01:02
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16 Jul 2024 04:37