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arXiv · 1107.5208

Pseudodifferential operators on periodic graphs

Vladimir S. Rabinovich·Steffen Roch
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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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Vladimir S. Rabinovich, Steffen Roch. 2011-07-26. Pseudodifferential operators on periodic graphs. https://arxiv.org/abs/1107.5208

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