In recent papers a number of authors have considered Borel probability
measures μ in \br^d such that the Hilbert space L2(μ) has a Fourier
basis (orthogonal) of complex exponentials. If μ satisfies this property,
the set of frequencies in this set are called a spectrum for μ. Here we fix
a spectrum, say Γ, and we study the possibilities for measures μ
having Γ as spectrum.Comment: v