Preservers of totally positive kernels and Pólya frequency functions

Belton, Alexander and Guillot, Dominique and Khare, Apoorva and Putinar, Mihai (2022) Preservers of totally positive kernels and Pólya frequency functions. Mathematics Research Reports, 3. pp. 35-56. ISSN 2772-9559

Full text not available from this repository.

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.

Item Type:
Journal Article
Journal or Publication Title:
Mathematics Research Reports
Subjects:
ID Code:
173783
Deposited By:
Deposited On:
28 Jul 2022 15:05
Refereed?:
Yes
Published?:
Published
Last Modified:
22 Nov 2022 11:40