Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An application of the Schur algorithm to variability regions of certain
  analytic functions   Let $\Omega$ be a convex domain in the complex plane ${\mathbb C}$ with
$\Omega \not= {\mathbb C}$, and $P$ be a conformal map of the unit disk
${\mathbb D}$ onto $\Omega$. Let ${\mathcal F}_\Omega$ be the class of analytic
functions $g$ in ${\mathbb D}$ with $g({\mathbb D}) \subset \Omega$, and
$H_1^\infty ({\mathbb D})$ be the closed unit ball of the Banach space
$H^\infty ({\mathbb D})$ of bounded analytic functions $\omega$ in ${\mathbb
D}$, with norm $\| \omega \|_\infty = \sup_{z \in {\mathbb D}} |\omega (z)|$.
Let ${\mathcal C}(n) = \{ (c_0,c_1 , \ldots , c_n ) \in {\mathbb C}^{n+1}:
\text{there exists} \; \omega \in H_1^\infty ({\mathbb D}) \; \text{satisfying}
\; \omega (z) = c_0+c_1z + \cdots + c_n z^n + \cdots$ for ${z\in \mathbb D}\}$.
For each fixed $z_0 \in {\mathbb D}$, $j=-1,0,1,2, \ldots$ and $c = (c_0, c_1 ,
\ldots , c_n) \in {\mathcal C}(n)$, we use the Schur algorithm to determine the
region of variability $V_\Omega^j (z_0, c ) = \{ \int_0^{z_0}
z^{j}(g(z)-g(0))\, d z : g \in {\mathcal F}_\Omega \; \text{with} \; (P^{-1}
\circ g) (z) = c_0 +c_1z + \cdots + c_n z^n + \cdots \}$. We also show that for
$z_0 \in {\mathbb D} \backslash \{ 0 \}$ and $c \in \textrm{Int} \, {\mathcal
C}(n) $, $V_\Omega^j (z_0, c )$ is a convex closed Jordan domain, which we
determine by giving a parametric representation of the boundary curve $\partial
V_\Omega^j (z_0, c )$.

0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con