Abstract
It is known that a necessary condition for $T:=\sum Q_k(x) D^k$ to be hyperbolicity preserving is that $Q_k(x)$ and $Q_{k-1}(x)$ have interlacing zeros. We characterize all quadratic linear operators; as a consequence, we find several classes of the $P_n$-multiplier sequence.
Citation
R. Bates. R. Yoshida. "Quadratic hyperbolicity preservers and multiplier sequences." Rocky Mountain J. Math. 46 (1) 51 - 72, 2016. https://doi.org/10.1216/RMJ-2016-46-1-51
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