10 problems

The LFED Conjecture. Images of locally finite $K$-derivations and $K$-$\mathcal{E}$-derivations of $K$-algebras are Mathieu subspaces.

Let $K$ be a field of characteristic zero, and let $z=(z_1,z_2,\dots,z_n)$ be $n$ commuting indeterminates. For a commutative $K$-algebra ${\mathcal A}$ and a $K$-subspace $V$ of…

Let $A={\mathbb C}[\xi,z]$, where $\xi=(\xi_1,\ldots,\xi_m)$ and $z=(z_1,\ldots,z_m)$ are two sets of commuting indeterminates. For each $i$, define…

Integral conjecture. The subspace $V_B(\sigma)$ is a Mathieu subspace of $\mathbb C[t]$. This is one of the one-dimensional Integral and Image Conjectures; the source records speci…

Image Conjecture. The image of $\mathcal D$ is a Mathieu subspace of $B$.

Let ${\bf k}\in\mathbb N^n$, and let $L^{[\bf k]}_\alpha(z)$ denote the generalized Laguerre polynomials for multi-indices $\alpha\in\mathbb N^n$. Let $\mathcal M$ be the subspace…

For $t\in\mathbb C$, let $\mathcal B_t[\xi,z]$ be the algebra on the vector space $\mathbb C[\xi,z]$ with product $\ast_t$, and set … A subspace of a commutative algebra is a Mathi…

Let $t\in\mathbb C$, and let … be the image of the commuting differential operators $(\xi_i-t\partial_i)$. A subspace $\mathcal M$ of a commutative algebra $\mathcal A$ is a Mathie…

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…

The generalized image conjecture. The subspace $\operatorname{Im}'\Lambda$ is a Mathieu subspace of $\mathbb C[z]$. The paper notes that this generalizes the image conjecture and p…