Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shannon Sampling and Parseval Frames on Compact Manifolds   Our article is a summary of some results for Riemannian manifolds that were
obtained in \cite{gpes}-\cite{Pesssubm}. To the best of our knowledge these are
the pioneering papers which contain the most general results about frames,
Shannon sampling, and cubature formulas on compact and non-compact Riemannian
manifolds. In particular, the paper \cite{gpes} gives an "end point"
construction of tight localized frames on homogeneous compact manifolds. The
paper \cite{Pessubm} is the first systematic development of localized frames on
compact domains in Euclidean spaces.

10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ