Shift-invariant subspaces an wavelets on local fields (Q2400081)

Let \(\mathbb{K}\) be a local field of positive characteristic which is locally compact, nondiscrete and totally disconnected. Let \(\Lambda\) be a certain additive subgroup of \(\mathbb{K}\) called a translation set. The author show that every closed shift-invariant subspace of \(L^2 (\mathbb{K})\) is generated by the \(\Lambda\)-translates of a countable number of functions. This result is used to provide a characterization of wavelets on the field \(\mathbb{K}\).