A panorama of positivity. II:fixed dimension

Belton, Alexander and Guillot, Dominique and Khare, Apoorva and Putinar, Mihai (2020) A panorama of positivity. II:fixed dimension. In: Complex Analysis and Spectral Theory. Contemporary Mathematics . American Mathematical Society, Providence, RI, pp. 109-150. ISBN 9781470446925

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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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10 Feb 2020 10:35
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20 Sep 2023 02:29