On 2D Inverse Problems/Fourier coordinates
For an integer N, let be a not unit N'th root of unity.
We consider the following Fourier transform given by the symmetric Vandermonde matrix:
The square of the Fourier transform is the identity:
Exercise (*). If a network is rotation invariant then its Dirichlet-to-Neumann operator is diagonal in Fourier coordinates. (Hint) The harmonic functions commute are rotation invariant.