  We extend Robertson's theorem to apply to frames generated by the action of a
discrete, countable abelian unitary group. Within this setup we use Stone's
theorem and the theory of spectral multiplicity to analyze wandering frame
collections. Motivated by wavelet theory, we explicitly apply our results to
the action of the integers given by translations on $\ltwo$. This yields a new
functional analytic method of constructing a wavelet from a multiresolution
analysis.
