Reproducing subgroups of Sp(2,R). Part II: admissible vectors

In part I we introduced the class E_2 of Lie subgroups of Sp(2,R) and obtained a classification up to conjugation ( see Theorem 6 below). Here, we determine for which of these groups the restriction of the metaplectic representation gives rise to a reproducing formula. In all the positive cases we characterize the admissible vectors with a generalized Calder\uf3n equation. They include products of 1D-wavelets, directional wavelets, shearlets, and many new examples