Belton, Alexander ; Guillot, Dominique ; Khare, Apoorva ; Putinar, Mihai (2020) A panorama of positivity. II: Fixed dimension Contemporary Mathematics, 743 . pp. 109-150. ISSN 0271-4132
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Official URL: http://doi.org/10.1090/conm/743/14958
Related URL: http://dx.doi.org/10.1090/conm/743/14958
Abstract
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.
Item Type: | Article |
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Source: | Copyright of this article belongs to American Mathematical Society. |
ID Code: | 127311 |
Deposited On: | 17 Oct 2022 05:11 |
Last Modified: | 17 Oct 2022 05:11 |
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