Order-preservation conjecture for generalized Bochner–Krall operators

Let $L$ be an irreducible differential operator of order $k$ solving the generalized Bochner–Krall problem, and let $\Lambda$ be its corresponding difference operator. Order-preservation conjecture. For any irreducible differential operator $L$ of order $k$ solving the generalized Bochner–Krall problem, the order of the corresponding difference operator $\Lambda$ is also $k$. This conjectural claim concerns the relation between the differential and difference formulations of the generalized problem; its resolution is not supplied in the source.