Admissible vectors and Radon-Nikodym theorems

Abstract

Admissible vectors lead to frames or coherent states under the action of a group by means of square integrable representations. This work shows that admissible vectors can be seen as weights with central support on the (left) group von Neumann algebra. The analysis involves spatial and cocycle derivatives, noncommutative $L^p$-Fourier transforms and Radon-Nikodym theorems. Square integrability confine the weights in the predual of the algebra and everything may be written in terms of a (right selfdual) bounded element.