For an integer *N*, let be a not unit *N'*th root of unity.

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We consider the following **Fourier transform** given by the symmetric **Vandermonde matrix**:

For example,

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.