Preservers of totally positive kernels and Polya frequency functions

Autor:	Belton, Alexander, Guillot, Dominique, Khare, Apoorva, Putinar, Mihai
Rok vydání:	2021
Předmět:	Mathematics - Functional Analysis Mathematics - Classical Analysis and ODEs Mathematics - Probability Mathematics - Rings and Algebras 15B48 (primary) 15A15 39B62 42A82 44A10 47B34 (secondary)
Zdroj:	Mathematics Research Reports 3 (2022), 35-56
Druh dokumentu:	Working Paper
DOI:	10.5802/mrr.12
Popis:	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. Comment: 25 pages, no figures. This is an announcement of some of the results in a sequence of three closely related recent papers arXiv:2006.16213, arXiv:2008.05121, and arXiv:2101.02129. Final version, published in Mathematics Research Reports
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2110.08206 Zobrazit plný text záznamu View this record from Arxiv