Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-commutative holomorphic functions on Operator domains   We characterize functions of $d$-tuples of bounded operators on a Hilbert
space that are uniformly approximable by free polynomials on balanced open
sets.

16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org