Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral theory of the multi-frequency quasi-periodic operator with a
  Gevrey type perturbation   In this paper, we study the multi-frequency quasi-periodic operator with a
Gevrey type perturbation. We first establish the large deviation theorem (LDT)
for the multi-dimensional operator with a sub-exponential (or Gevrey)
long-range hopping and then prove the pure point spectrum property. Based on
the LDT and the Aubry duality, we show the absence of point spectrum for the
$1D$ exponential long-range operator with a multi-frequency and a Gevrey
potential. We also prove the spectrum has the positive Lebesgue measure.

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The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
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The categories of this paper are: eess
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn