Amplitude maximization in stable systems, Schur positivity, and some conjectures on polynomial interpolation

Dmitrii M. Ostrovskii, Pavel S. Shcherbakov

For $r>0$ and integers $t\ge n>0$, we consider the following problem: maximize the amplitude $|x_t|$ at time $t$, over all complex solutions $x=(x_0,x_1,\dots )$ of arbitra…