# Tagged Questions

**10**

votes

**2**answers

406 views

### Codimension of the range of certain linear operators

Assume that $P(x,y), Q(x,y) \in \mathbb{R}[x,y]$ are two polynomials. We define a linear map
$D$ on $\mathbb{R}[x,y]$ with $D(U)=PU_{x}+QU_{y}$. In fact $D$ is the derivational operator correspond ...

**1**

vote

**1**answer

260 views

### Modules over rings of differential operators

If $M$ is a left $\mathbb{C}[t] \langle \partial _t \rangle$-module ( a left module over the Weyl algebra), then $\mathrm{Hom}(M,\mathbb{C}[t] \langle \partial _t \rangle)$ is equipped with a ...

**10**

votes

**1**answer

388 views

### Does the image of a differential operator always contain an ideal?

Let $\delta$ denote a non-zero complex algebraic differential operator in a single variable x. That is, it can be written as a sum
$$ \delta = \sum_i f_i\partial_x^i$$
where there $f_i$ are complex ...