Total-positivity preservers
Functional Analysis
2020-06-25 v3 Classical Analysis and ODEs
Rings and Algebras
Abstract
We prove that the only entrywise transforms of rectangular matrices which preserve total positivity or total non-negativity are either constant or linear. This follows from an extended classification of preservers of these two properties for matrices of fixed dimension. We also prove that the same assertions hold upon working only with symmetric matrices; for total-positivity preservers our proofs proceed through solving two totally positive completion problems.
Keywords
Cite
@article{arxiv.1711.10468,
title = {Total-positivity preservers},
author = {Alexander Belton and Dominique Guillot and Apoorva Khare and Mihai Putinar},
journal= {arXiv preprint arXiv:1711.10468},
year = {2020}
}
Comments
This paper is being completely rewritten, with the focus now on kernels on arbitrary domains, and the ensuing analysis. This includes Polya frequency functions/sequences, Hankel and other Toeplitz kernels, and the study of their preservers