Abstract

This work is a contribution to the general theory of frames, using group representations. Specifically, we use the theory of generalized coherent states for semidirect product groups to construct coherent states for the three dimensional Euclidean group, starting from a representation of this group, induced from a representation of the subgroup H = [Special characters omitted.] {604} SO (2). Families of continuous coherent states are explicitly constructed for two specific choices of sections from the coset space w = E (3)/(T 3 {604} SO 3 (2)) to the group. We also discuss admissibility conditions for the existence of continuous frames for the general class of affine sections. Next we propose a discretization procedure for these continuous frames. Once again we obtain general admissibility conditions for the existence of frames and in particular, tight frames. Explicit examples are worked out.