Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Surjectivity of differential operators and linear topological invariants
  for spaces of zero solutions   We provide a sufficient condition for a linear differential operator with
constant coefficients $P(D)$ to be surjective on $C^\infty(X)$ and
$\mathscr{D}'(X)$, respectively, where $X\subseteq\mathbb{R}^d$ is open.
Moreover, for certain differential operators this sufficient condition is also
necessary and thus a characterization of surjectivity for such differential
operators on $C^\infty(X)$, resp. on $\mathscr{D}'(X)$, is derived.
Additionally, we obtain for certain surjective differential operators $P(D)$ on
$C^\infty(X)$, resp. $\mathscr{D}'(X)$, that the spaces of zero solutions
$C_P^\infty(X)=\{u\in C^\infty(X);\, P(D)u=0\}$, resp.
$\mathscr{D}_P'(X)=\{u\in\mathscr{D}'(X);\,P(D)u=0\}$ possess the linear
topological invariant $(\Omega)$ introduced by Vogt and Wagner in [27], resp.
its generalization $(P\Omega)$ introduced by Bonet and Doma\'nski in [1].

11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics