7 problems

Scalarity conjecture. This result should hold for arbitrary $N$: the algebra $\mathcal{D}(W)$ contains only scalar operators of order zero.

Conjecture. The algebra $\mathcal{D}$ coincides with the subalgebra $\mathcal{A}$:

Let $\Sigma\in\mathcal M_{p,1}(\mathbb T)$ have infinite support, and let $(\boldsymbol\alpha_k)_{k\geq0}\in(\mathbb B_p)^{\mathbb N_0}$ be its matrix Verblunsky coefficients. Let…

Explicit lowest-spherical-function conjecture. For all $n\geq 3$,

The second family is a one-parameter sequence of $2\times2$ matrix-valued orthogonal polynomials obtained from the compact Gelfand pair … and spherical functions of type…

Let $W$ be the matrix weight under consideration, and let $\mathcal D(W)$ denote its algebra of differential operators. The paper constructs four differential operators…

Let $W$ be the matrix weight under consideration, and let $\mathcal D(W)$ denote its algebra of differential operators. Let $D_1,D_2,D_3,D_4$ be the four differential operators of…