Zhirayr Avetisyan (UCL)

On the correspondence between harmonic analysis and spectral theory

The spectral theory of an invariant operator in a homogeneous space naturally interferes with group harmonic analysis in that space. For particular classes of homogeneous spaces the correspondence between the two have been described long ago, but the general case remains open. In this talk we will discuss aproaches to this correspondence for general Lie groups, and will look at explicit examples on Bianchi groups. Moreover, we will see how this correspondence reflects the consistency of the notion of an elementary particle in mathematical cosmology.