  Let G be a locally compact abelian group with compact open subgroup H. The
best known example of such a group is G=Q_p, the field of p-adic rational
numbers (as a group under addition), which has compact open subgroup H=Z_p, the
ring of p-adic integers. Classical wavelet theories, which require a
non-trivial discrete subgroup for translations, do not apply to G, which may
not have such a subgroup. A wavelet theory is developed on G using coset
representatives of a quotient of the dual group of G. Wavelet bases are
constructed by means of an iterative method giving rise to so-called wavelet
sets in the dual group.
