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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Preservers of totally positive kernels and Pólya frequency functions
AU - Belton, Alexander
AU - Guillot, Dominique
AU - Khare, Apoorva
AU - Putinar, Mihai
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.
KW - Totally non-negative function
KW - totally positive function
KW - totally non-negative kernel
KW - totally positive kernel
KW - totally non-negative matrix
KW - totally positive matrix
KW - entrywise transformation
KW - Pólya frequency function
KW - Pólya frequency sequence
KW - Hirschman–Widder density
KW - exponential random variable
KW - spherical function
KW - orbital integral
KW - multivariate statistics
U2 - 10.5802/mrr.12
DO - 10.5802/mrr.12
M3 - Journal article
VL - 3
SP - 35
EP - 56
JO - Mathematics Research Reports
JF - Mathematics Research Reports
SN - 2772-9559
ER -