Linear operators preserving volume polynomials

Abstract

We study linear operators preserving the property of being a volume polynomial. More, precisely we show that a linear operator preserves this property if the associated symbol is itself a volume polynomial. This can be seen as an analogue to theorems by Borcea-Brändén and Brändén-Huh for stable polynomials and Lorentzian polynomials, respectively.

11 pages, this manuscript is now superseded by arXiv:2506.22415