Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the nuclearity of weighted spaces of smooth functions   Nuclearity plays an important role for the Schwartz kernel theorem to hold
and in transferring the surjectivity of a linear partial differential operator
from scalar-valued to vector-valued functions via tensor product theory. In
this paper we study weighted spaces $\mathcal{EV}(\Omega)$ of smooth functions
on an open subset $\Omega\subset\mathbb{R}^{d}$ whose topology is given by a
family of weights $\mathcal{V}$. We derive sufficient conditions on the weights
which make $\mathcal{EV}(\Omega)$ a nuclear space.

5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
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
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph