Preservers of totally positive kernels and Pólya frequency functions

Belton, Alexander and Guillot, Dominique and Khare, Apoorva and Putinar, Mihai (2022) Preservers of totally positive kernels and Pólya frequency functions. Mathematics Research Reports, 3. pp. 35-56. ISSN 2772-9559

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Fractional powers and polynomial maps preserving structured totally positive matrices, one-sided Pólya frequency functions, or totally positive kernels are treated from a unifying perspective. Besides the stark rigidity of the polynomial transforms, we unveil an ubiquitous separation between discrete and continuous spectra of such inner fractional powers. Classical works of Schoenberg, Karlin, Hirschman, and Widder are completed by our classification. Concepts of probability theory, multivariate statistics, and group representation theory naturally enter into the picture.

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Mathematics Research Reports
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28 Jul 2022 15:05
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22 Nov 2022 11:40