6 problems

Let $T$ be a pure finite-rank commuting $n$-contraction, and let ${\mathcal H}_n(T)$ be its corresponding analytic module. The degree of $T$ is the degree of the polynomial…

Commutativity conjecture. For general $n\geq 2$, one has

Commutativity conjecture. The family of operators $I(\alpha)$ is commutative on ${\cal F}_n$; equivalently, $[I(\alpha),I(\beta)]=0$.

Let $H$ be a Hilbert space, let $T_1,T_2\in B(H)$ commute, and suppose that $\\{T_1^iT_2^j\varphi\\}_{i,j\geq 0}$ is an overcomplete frame for $H$. Let $R_1$ and $R_2$ be the assoc…

Let $H$ be a Hilbert space, let $T_1,T_2\in B(H)$ commute, and suppose that $\\{T_1^iT_2^j\varphi\\}_{i,j\geq 0}$ is a frame for $H$ satisfying the conditions of Lemma. The iterati…

The theory concerns commutative subalgebras of a completion of the algebra of partial differential operators in two variables, with the rank of a subalgebra measuring the correspon…