Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Clarkson-Erd\"os-Schwartz Theorem on a Sector   We prove a Clarkson-Erd\"os-Schwartz type theorem for the case of a closed
sector in the plane. Concretely, we get some sufficient conditions for the
incompleteness and minimality of a M\"untz system
$E(\Lambda)={z^{\lambda_n}:n=0,1,...}$ in the space $H_\alpha$, where
$H_\alpha=A(I_\alpha)$, $I_\alpha={z\in\mathbb{C}:|\arg (z)|\leq \alpha
\text{and} |z|\leq 1}$ and $A(K)=C(K)\cap H(\textbf{Int}[K])$ denotes the space
of continuous functions on the compact set $K$ which are analytic in the
interior of $K$. Furthermore, we prove that, if $\textbf{span}[E(\Lambda)]$ is
not dense in $H_\alpha$ then all functions $f\in
\bar{\textbf{span}}[E(\Lambda)]$ can be analytically extended to the interior
of the sector $I_\pi$.

10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph