Speaker
Description
Spaces invariant under unitary group representations have been extensively studied in the recent decades due to their importance in various areas, such as the theory of Gabor systems, wavelets and approximation theory. Dual integrable representations form a large and important class among the unitary representations, for which the properties of the cyclic subspaces and their generating orbits can be described in terms of the associated bracket map; the existence of an operative bracket map is, thefore, crucial for the utility of the definition. The concept was first introduced and studied for the abelian groups, and later for some specific classes in the non-commutative setting. We have recently introduced the definition for the entire class of locally compact groups. Being based on the non-commutative integration theory, the methods in the non-abelian case are quite different from the ones in the abelian setting; however, most of the main properties and fundamental results remain valid or have the appropriate analogues. In this talk, we present the main results concerned with the study of the dual integrability.
The talk is based on joint work with Hrvoje Šikić.
