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Preservers of totally positive kernels and Pólya frequency functions

Lookup NU author(s): Emeritus Professor Mihai Putinar

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This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).

Abstract

Fractional powers and polynomial maps preserving structured totally positive matrices, one-sided Polya 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.

Publication metadata

Author(s): Belton A, Guillot D, Khare A, Putinar M

Publication type: Article

Publication status: Published

Journal: Mathematical Research Reports

Year: 2022

Volume: 3

Pages: 35-56

Online publication date: 26/07/2022

Acceptance date: 03/06/2022

Date deposited: 18/10/2022

ISSN (electronic): 2772-9559

Publisher: Mathematics in Open Access

URL: https://doi.org/10.5802/mrr.12

DOI: 10.5802/mrr.12

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Funding

Funder referenceFunder name
DST/SJF/MS/2019/3
F.510/25/CAS-II/2018(SAP-I)
SB/SJF/2019-20/14
Simons Foundation
SB/S2/RJN-121/2017
University of Delaware Research Foundation

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