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Preservers of totally positive kernels and Pólya frequency functions

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Preservers of totally positive kernels and Pólya frequency functions. / Belton, Alexander; Guillot, Dominique; Khare, Apoorva et al.

In: Mathematics Research Reports, Vol. 3, 26.07.2022, p. 35-56.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Harvard

Belton, A, Guillot, D, Khare, A & Putinar, M 2022, 'Preservers of totally positive kernels and Pólya frequency functions', Mathematics Research Reports, vol. 3, pp. 35-56. https://doi.org/10.5802/mrr.12

APA

Belton, A., Guillot, D., Khare, A., & Putinar, M. (2022). Preservers of totally positive kernels and Pólya frequency functions. Mathematics Research Reports, 3, 35-56. https://doi.org/10.5802/mrr.12

Vancouver

Belton A, Guillot D, Khare A, Putinar M. Preservers of totally positive kernels and Pólya frequency functions. Mathematics Research Reports. 2022 Jul 26;3:35-56. doi: 10.5802/mrr.12

Author

Belton, Alexander ; Guillot, Dominique ; Khare, Apoorva et al. / Preservers of totally positive kernels and Pólya frequency functions. In: Mathematics Research Reports. 2022 ; Vol. 3. pp. 35-56.

Bibtex

@article{a1d968fa6ef54356a74ef77de769340a,
title = "Preservers of totally positive kernels and P{\'o}lya frequency functions",
abstract = "Fractional powers and polynomial maps preserving structured totally positive matrices, one-sided P{\'o}lya 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.",
keywords = "Totally non-negative function, totally positive function, totally non-negative kernel, totally positive kernel, totally non-negative matrix, totally positive matrix, entrywise transformation, P{\'o}lya frequency function, P{\'o}lya frequency sequence, Hirschman–Widder density, exponential random variable, spherical function, orbital integral, multivariate statistics",
author = "Alexander Belton and Dominique Guillot and Apoorva Khare and Mihai Putinar",
year = "2022",
month = jul,
day = "26",
doi = "10.5802/mrr.12",
language = "English",
volume = "3",
pages = "35--56",
journal = "Mathematics Research Reports",
issn = "2772-9559",

}

RIS

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 -