Reproducing subgroups of Sp(2,R). Part II: admissible vectors
Representation Theory
2014-03-07 v1
Abstract
In part I we introduced the class of Lie subgroups of 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 Calder\'on equation. They include products of 1D-wavelets, directional wavelets, shearlets, and many new examples.
Keywords
Cite
@article{arxiv.1212.2743,
title = {Reproducing subgroups of Sp(2,R). Part II: admissible vectors},
author = {Giovanni S. Alberti and Filippo De Mari and Ernesto De Vito and Lucia Mantovani},
journal= {arXiv preprint arXiv:1212.2743},
year = {2014}
}
Comments
37 pages, 3 figures