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Preservers of totally positive kernels and Pólya frequency functions

Research output: Contribution to Journal/MagazineJournal articlepeer-review

<mark>Journal publication date</mark>26/07/2022
<mark>Journal</mark>Mathematics Research Reports
Number of pages22
Pages (from-to)35-56
Publication StatusPublished
<mark>Original language</mark>English


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.