PUB - Publikationen an der Universität Bielefeld

Several classes of tempered measures are characterised that are eigenmeasures of the Fourier transform, the latter viewed as a linear operator on (generally unbounded) Radon measures on R-d. In particular, we classify all periodic eigenmeasures on R, which gives an interesting connection with the discrete Fourier transform and its eigenvectors, as well as all eigenmeasures on R with uniformly discrete support. An interesting subclass of the latter emerges from the classic cut and project method for aperiodicMeyer sets. Finally, we construct a large class of eigenmeasures with locally finite support that is not uniformly discrete and has large gaps around 0.