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

Published

Complex Analysis and Spectral Theory. ed. / H. Garth Dales; Dmitry Khavinson; Javad Mashreghi. Providence, RI: American Mathematical Society, 2020. p. 109-150 (Contemporary Mathematics; Vol. 743).

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

Belton, A, Guillot, D, Khare, A & Putinar, M 2020, A panorama of positivity. II: fixed dimension. in HG Dales, D Khavinson & J Mashreghi (eds), *Complex Analysis and Spectral Theory.* Contemporary Mathematics, vol. 743, American Mathematical Society, Providence, RI, pp. 109-150. https://doi.org/10.1090/conm/743/14958

Belton, A., Guillot, D., Khare, A., & Putinar, M. (2020). A panorama of positivity. II: fixed dimension. In H. G. Dales, D. Khavinson, & J. Mashreghi (Eds.), *Complex Analysis and Spectral Theory *(pp. 109-150). (Contemporary Mathematics; Vol. 743). American Mathematical Society. https://doi.org/10.1090/conm/743/14958

Belton A, Guillot D, Khare A, Putinar M. A panorama of positivity. II: fixed dimension. In Dales HG, Khavinson D, Mashreghi J, editors, Complex Analysis and Spectral Theory. Providence, RI: American Mathematical Society. 2020. p. 109-150. (Contemporary Mathematics). doi: 10.1090/conm/743/14958

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title = "A panorama of positivity. II: fixed dimension",

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.",

author = "Alexander Belton and Dominique Guillot and Apoorva Khare and Mihai Putinar",

year = "2020",

month = mar,

day = "31",

doi = "10.1090/conm/743/14958",

language = "English",

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series = "Contemporary Mathematics",

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pages = "109--150",

editor = "Dales, {H. Garth} and Dmitry Khavinson and Javad Mashreghi",

booktitle = "Complex Analysis and Spectral Theory",

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N2 - 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.

AB - 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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