A New Class of Non-Linear Stability Preserving Operators

TL;DR

This paper introduces a new class of non-linear operators that maintain weak Hurwitz stability and the Laguerre-Pólya class, extending previous stability-preserving results in complex analysis.

Contribution

It generalizes Bränden's recent proof by defining a novel class of non-linear operators with stability-preserving properties.

Findings

New class of non-linear operators preserving stability

Extension of Bränden's proof of Stanley's conjecture

Operators maintain weak Hurwitz stability and Laguerre-Pólya class

Abstract

We extend Br\"and\'en's recent proof of a conjecture of Stanley and describe a new class of non-linear operators that preserve weak Hurwitz stability and the Laguerre-P\'olya class.