ORCID
- Belton, Alex: 0000-0002-4925-8294
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
2022-07-26
Publication Title
Mathematics Research Reports
Volume
3
Embargo Period
2023-02-23
Organisational Unit
School of Engineering, Computing and Mathematics
First Page
35
Last Page
56
Recommended Citation
Belton, A., Guillot, D., Khare, A., & Putinar, M. (2022) 'Preservers of totally positive kernels and Pólya frequency functions', Mathematics Research Reports, 3, pp. 35-56. Available at: https://doi.org/10.5802/mrr.12
