Sufficient conditions for a linear operator on $\mathbb{R}[x]$ to be monotone

preprint2016arXivOpen access

We demonstrate that being a hyperbolicity preserver does not imply monotonicity for infinite order differential operators on $\mathbb{R}[x]$ , thereby settling a recent conjecture in the negative. We also give some sufficient conditions for such operators to be monotone.

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Sufficient conditions for a linear operator on $\mathbb{R}[x]$ to be monotone

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Sufficient conditions for a linear operator on $\mathbb{R}[x]$ to be monotone