Harmonic analysis on : Part II

Harmonic analysis on GF ( p p ∞ ) is studied. The Heisenberg–Weyl HW [ G ˆ , GF ( p p ∞ ) , G ˆ ] group of displacements is shown to be a locally compact and totally disconnected topological group. The formalism introduces algebraic concepts from the theory of Galois fields into harmonic analysis. For example, a Galois group of Frobenius transformations on functions, analogous to the Galois group of Frobenius transformations in Galois theory, is introduced into harmonic analysis. A larger group which we call Heisenberg–Weyl–Galois group is also discussed.