On 2D Inverse Problems/ An infinite example
The following construction provides an example of an infinite graph, which Dirichlet-to-Neumann operator satisfies the operator equation in the title of this chapter.
The operator equation reflects the self-duality and self-symmetry of the infinite graph.
![](http://upload.wikimedia.org/wikipedia/commons/thumb/3/36/Graph_and_dual.jpg/220px-Graph_and_dual.jpg)
Exercise (**). Prove that the Dirichlet-to-Neumann operator of the graph with the natural boundary satisfies the functional equation. (Hint) Use the fact that the operator/matrix is the fixed point of the Schur complement
where
is the circular matrix of first differences.