Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unitarization of the Horocyclic Radon Transform on Symmetric Spaces   We consider the Radon transform for a dual pair $(X,\Xi)$, where $X=G/K$ is a
noncompact symmetric space and $\Xi$ is the space of horocycles of $X$. We
address the unitarization problem that was considered (and solved in some
cases) by Helgason, namely the determination of a pseudo-differential operator
such that the pre-composition with the Radon transform extends to a unitary
operator $\mathcal{Q}\colon L^2(X)\to L_\flat^2(\Xi)$, where $L_\flat^2(\Xi)$
is a closed subspace of $L^2(\Xi)$ which accounts for the Weyl symmetries.
Furthermore, we show that the unitary extension intertwines the quasi-regular
representations of $G$ on $L^2(X)$ and $L_\flat^2(\Xi)$.

15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio