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Lookup NU author(s): Professor Mihai Putinar
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© 2020 American Mathematical Society. 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.
Author(s): Belton A, Guillot D, Khare A, Putinar M
Editor(s): H. Garth Dales, Dmitry Khavinson, Javad Mashreghi
Publication type: Book Chapter
Publication status: Published
Book Title: Complex Analysis and Spectral Theory
Year: 2020
Volume: 743
Pages: 109-150
Print publication date: 30/03/2020
Acceptance date: 02/04/2018
Series Title: Contemporary Mathematics
Publisher: American Mathematical Society
Place Published: Providence, RI
URL: https://doi.org/10.1090/conm/743/14958
DOI: 10.1090/conm/743/14958
Library holdings: Search Newcastle University Library for this item
ISBN: 9781470446925
