Dynamical systems on translation bounded measures: pure point dynamical and diffraction spectra

Baake M, Lenz D. Dynamical systems on translation bounded measures: pure point dynamical and diffraction spectra. ERGODIC THEORY AND DYNAMICAL SYSTEMS. 2004;24:1867-1893.Certain topological dynamical systems that arise from actions of or-compact locally compact Abelian groups on compact spaces of translation bounded measures are considered. Such a measure dynamical system is shown to have a pure point dynamical spectrum if and only if its diffraction spectrum is pure point