Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral projectors, resolvent, and Fourier restriction on the
  hyperbolic space   We develop a unified approach to proving $L^p-L^q$ boundedness of spectral
projectors, the resolvent of the Laplace-Beltrami operator and its derivative
on $\mathbb{H}^d.$ In the case of spectral projectors, and when $p$ and $q$ are
in duality, the dependence of the implicit constant on $p$ is shown to be
sharp. We also give partial results on the question of $L^p-L^q$ boundedness of
the Fourier extension operator. As an application, we prove smoothing estimates
for the free Schr\"{o}dinger equation on $\mathbb{H}^d$ and a limiting
absorption principle for the electromagnetic Schr\"{o}dinger equation with
small potentials.

4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org