4 problems

Scalar corona conjecture. There exist $p_j\in M(\mathbb{R}_-)$ for $j=1,\dots,k$ such that

Let $\Omega=\mathbb{B}^n$, let $V$ be the common zero set of some functions in Hardy space $H^2(\mathbb{B}^n)$, and let $M_V^\bot$ be the quotient Drury–Arveson submodule with mult…

Let $\mathbb{B}_n$ be the unit ball in $\mathbb{C}^n$, let $B_p^\sigma(\mathbb{B}_n)$ be the relevant Besov space, and let…

Let $C\langle X_1,\ldots,X_d\rangle$ be the algebra of functions on the polydisc $\Delta^d$, and let $g_1,\ldots,g_n$ belong to it. Write $(g_1,\ldots,g_n)$ and $(X_1,\ldots,X_d)$…