  Spectral measures give rise to a natural harmonic analysis on the unit disc
via a boundary representation of a positive matrix arising from a spectrum of
the measure. We consider in this paper the reverse: for a positive matrix in
the Hardy space of the unit disc we consider which measures, if any, yield a
boundary representation of the positive matrix. We introduce a potential
characterization of those measures via a matrix identity and show that the
characterization holds in several important special cases.
