ORCID

Abstract

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.

DOI

10.5802/mrr.12

Publication Date

2022-01-01

Publication Title

Mathematics Research Reports

Volume

3

First Page

35

Last Page

56

Embargo Period

2023-02-23

Organisational Unit

School of Engineering, Computing and Mathematics

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