Multi-resolution analysis and fractional quantum Hall effect: An equivalence result

In this article we prove that any multi-resolution analysis of ℒ2(R) produces, for some values of the filling factor, a single-electron wave function of the lowest Landau level (LLL) which, together with its (magnetic) translation, gives rise to an orthonormal set in the LLL. We also discuss the inverse construction. Moreover, we extend this procedure to the higher Landau levels and we discuss the analogies and the differences between this procedure and the one previously proposed by J.-P. Antoine and the author. © 2001 American Institute of Physics.