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A panorama of positivity. II: fixed dimension

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSNChapter (peer-reviewed)peer-review

Publication date31/03/2020
Host publicationComplex Analysis and Spectral Theory
EditorsH. Garth Dales, Dmitry Khavinson, Javad Mashreghi
Place of PublicationProvidence, RI
PublisherAmerican Mathematical Society
Number of pages42
ISBN (electronic)9781470454531
ISBN (print)9781470446925
<mark>Original language</mark>English

Publication series

NameContemporary Mathematics
PublisherAmerican 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.