Abstract
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 Γ 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 Γ. We apply these results to study the Fredholm property of a class of singular integral operators and of certain locally compact operators on graphs.
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