TY - JOUR
T1 - Preservers of totally positive kernels and Pólya frequency functions
AU - Belton, A
AU - Guillot, D
AU - Khare, A
AU - Putinar, M
PY - 2022/7/26
Y1 - 2022/7/26
N2 - 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.
AB - 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.
UR - https://pearl.plymouth.ac.uk/context/secam-research/article/1553/viewcontent/MRR_2022__3__35_0.pdf
U2 - 10.5802/mrr.12
DO - 10.5802/mrr.12
M3 - Article
SN - 2772-9559
VL - 3
SP - 35
EP - 56
JO - Mathematics Research Reports
JF - Mathematics Research Reports
IS - 0
ER -