REPRODUCING SUBGROUPS OF SP(2,R). PART II: ADMISSIBLE VECTORS.

Abstract. In part I we introduced the class E2 of Lie subgroups of Sp(2,R) and obtained a classification up to conjugation (Theorem 1.1). 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 Calderón equation. They include products of 1D-wavelets, directional wavelets, shearlets, and many new examples. 1