Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Magnetic pseudodifferential operators represented as generalized
  Hofstadter-like matrices   First, we reconsider the magnetic pseudodifferential calculus and show that
for a large class of non-decaying symbols, their corresponding magnetic
pseudodifferential operators can be represented, up to a global gauge
transform, as generalized Hofstadter-like, bounded matrices. As a by-product,
we prove a Calder\'on-Vaillancourt type result. Second, we make use of this
matrix representation and prove sharp results on the spectrum location when the
magnetic field strength $b$ varies. Namely, when the operators are
self-adjoint, we show that their spectrum (as a set) is at least
$1/2$-H\"{o}lder continuous with respect to $b$ in the Hausdorff distance.
Third, when the magnetic perturbation comes from a constant magnetic field we
show that their spectral edges are Lipschitz continuous in $b$. The same
Lipschitz continuity holds true for spectral gap edges as long as the gaps do
not close.

29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
3
The categories of this paper are: physics