The orthogonal-polynomial version of the Duistermaat–van der Kallen conjecture

Let $B\subset\mathbb R^n$, let $w(z)$ be a weight function, and let $\{u_\alpha\mid\alpha\in\mathbb N^n\}$ be a sequence of orthogonal polynomials over $B$. Let $\mathcal M$ be the subspace of $f(z)\in\mathbb C[z]$ whose coefficient of $u_0$ in its unique expansion in the $u_\alpha(z)$ is zero. The orthogonal-polynomial constant-term conjecture. The subspace $\mathcal M$ is a Mathieu subspace of the polynomial algebra $\mathbb C[z]$. Equivalently, it is the complex span of the $u_\alpha(z)$ with $\alpha\neq0$. The source presents this as a reformulation of the generalized Mathieu conjecture for the weight measure $w(z)\,dz$; no resolution is given in the supplied text.