Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on function algebras on disks   Let $D$ be a closed disk in the complex plane centered at the origin, $f, g$
complex valued continuous function on $D$. Let $P[f,g; D]$ (res. $R[f, g; D])$)
be the uniform closure on $D$ of polynomials (res. rational functions) in
variables $f$ and $g$. In \cite{OS}, using complex dynamical systems, O'Farrell
and Sanabria-Garcia proved that $\{\Big(z^2, \cfrac{\overline
z}{1+\overline{z}}\Big): z\in D\}$ is not polynomially convex with $D$ small
enough and so that $P[z^2,\cfrac{\overline z}{1+\overline z}; D]\ne C(D)$ if
$D$ is sufficient small. In this paper, we first give a certain conditions for
rational convexity of union of two compact set of $\Bbb C^n$ and apply to show
that $R[z^2, \cfrac{\overline z}{1+\overline z}; D]= C(D)$ for all $D$ small
enough

35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org