Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orthogonally additive polynomials on convolution algebras associated
  with a compact group   Let $G$ be a compact group, let $X$ be a Banach space, and let $P\colon
L^1(G)\to X$ be an orthogonally additive, continuous $n$-homogeneous
polynomial. Then we show that there exists a unique continuous linear map
$\Phi\colon L^1(G)\to X$ such that $P(f)=\Phi
\bigl(f\ast\stackrel{n}{\cdots}\ast f \bigr)$ for each $f\in L^1(G)$. We also
seek analogues of this result about $L^1(G)$ for various other convolution
algebras, including $L^p(G)$, for $1< p\le\infty$, and $C(G)$.

28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat