Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Limits of functions and elliptic operators   We show that a subspace $S$ of the space of real analytical functions on a
manifold that satisfies certain regularity properties is contained in the set
of solutions of a linear elliptic differential equation. The regularity
properties are that $S$ is closed in $L^2(M)$ and that if a sequence of
functions $f_n$ in $S$ converges in $L^2(M)$, then so do the partial
derivatives of the functions $f_n$.

30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph