Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On 1-cocycles induced by a positive definite function on a locally
  compact abelian group   For $\varphi$ a normalized positive definite function on a locally compact
abelian group $G$, we consider on the one hand the unitary representation
$\pi_\varphi$ associated to $\varphi$ by the GNS construction, on the other
hand the probability measure $\mu_\varphi$ on the Pontryagin dual $\hat{G}$
provided by Bochner's theorem. We give necessary and sufficient conditions for
the vanishing of 1-cohomology $H^1(G,\pi_\varphi)$ and reduced 1-cohomology
$\bar{H}^1(G,\pi_\varphi)$. For example, $\bar{H}^1(G,\pi_\varphi)=0$ if and
only if either $Hom(G,\mathbb{C})=0$ or $\mu_\varphi(1_G)=0$, where $1_G$ is
the trivial character of $G$.

3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom