February Fourier Talks 2010

Gestur Olafsson


Function spaces and representations


We present a unified framework for construction of Banach spaces of distributions from group representations, generalizing the construction by H. Feichtinger and K. H. Gröchenig in the 1980's. Spaces that can be described by this technique include the whole Banach-scale of Bergman spaces and Besov spaces on the light cone. The representation theory and the geometry of the group can be used to give unified way to give an atomic decomposition of those spaces.