A generalized spectral duality theorem (Q1189198)

The author studies a spectral duality theorem relating the point spectrum of a \(*\)-representation of a certain covariance algebra to the continuous spectrum of an associated family of \(*\)-representations. As an application, it is shown that if almost all the block operators associated with a real almost periodic function on \(R\) have pure point spectrum over a Borel subset of \(\mathbb{R}\), then almost all the Schrödinger operators with potentials belonging to the compact hull of the translation of this function have, over the same set, purely continuous spectrum.