Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pseudodifferential operators on periodic graphs   The main aim of the paper is Fredholm properties of a class of bounded linear
operators acting on weighted Lebesgue spaces on an infinite metric graph
$\Gamma$ which is periodic with respect to the action of the group ${\mathbb
Z}^n$. The operators under consideration are distinguished by their local
behavior: they act as (Fourier) pseudodifferential operators in the class
$OPS^0$ on every open edge of the graph, and they can be represented as a
matrix Mellin pseudodifferential operator on a neighborhood of every vertex of
$\Gamma$. We apply these results to study the Fredholm property of a class of
singular integral operators and of certain locally compact operators on graphs.

8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat