Belton, Alexander and Guillot, Dominique and Khare, Apoorva and Putinar, Mihai (2019) A panorama of positivity. I: dimension free. In: Analysis of Operators on Function Spaces. Trends in Mathematics . Birkhauser, Cham, pp. 117-165. ISBN 9783030146399
Full text not available from this repository.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.