Pseudodifferential operators on periodic graphs

Details Pseudodifferential operators on periodic graphs Pseudodifferential operators on periodic graphs

2011-07-26

arxiv.org/abs/1107.5208v1

Mathematics

Functional Analysis

22 pages

Scientific paper

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.

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