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 Calderón equation. They include products of 1D-wavelets, directional wavelets, shearlets, and many new examples.
Reproducing subgroups of Sp(2,R). Part II: admissible vectors
ALBERTI, GIOVANNI;DE MARI CASARETO DAL VERME, FILIPPO;DE VITO, ERNESTO;MANTOVANI, LUCIA
2013-01-01
Abstract
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 Calderón equation. They include products of 1D-wavelets, directional wavelets, shearlets, and many new examples.
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