Bases for the Space of Fixed Points of the Reed-Muller-Fourier Transform
We prove that the space of fixed points of the Reed-Muller-Fourier transform of n-variable functions on a p-element domain always has a basis. For odd p our proof is constructive and it proves the conjecture of C. Moraga, R. S. Stanković, M. Stanković and S. Stojković about the number of fixed points presented at ISMVL 2017. For even p we give a nonconstructive proof that relies on our earlier proof of the above mentioned conjecture.
Keywords: Reed-Muller-Fourier transform, eigenvector, eigenvalue, basis, fixed point, functions of several variables