Interlacing Properties of Coefficient Polynomials in Differential Operator Representations of Real-Root Preserving Linear Transformations

David A. Cardon, Evan L. Sorensen, Jason C. White

We study linear transformations $T:\mathbb{R}[x]\to \mathbb{R}[x]$ of the form $T[x^n]=P_n(x)$ where $\{P_n(x)\}$ is a real orthogonal polynomial system. Such transformatio…