Pseudodifferential operators on periodic graphs (Q421112)

The present paper is devoted to 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 pseudodifferential operators of a quite general class defined on a periodic graph. The main results concern Fredholm properties of those operators. Applications to singular integral operators and to a class of locally compact operators defined on graphs are also considered.