4 problems

Let $P(z)$ and $Q(z)$ be complex polynomials, and let $a,b\in\mathbb{C}$ with $a\neq b$ and $P(a)=P(b)$, $Q(a)=Q(b)$. For $i\geq 1$, define … The composition condition asserts that…

Let $P$ and $Q$ be complex polynomials and let $a,b$ be distinct complex numbers. A solution $Q$ of the polynomial moment problem is one satisfying … for every integer $i\geq 0$. A…

Let $P$ and $Q$ be polynomials, and consider the polynomial moment equations … A solution is called reducible if there exist polynomials $\widetilde P$, $\widetilde Q$, and $W$ wit…

Let $P(z)$ and $Q(z)$ be polynomials, and let $a,b$ be points satisfying $P(a)=P(b)$. A solution of system (1) is a polynomial $q(z)=Q'(z)$ satisfying the polynomial moment conditi…