Reproducing subgroups of Sp(2,R). Part II: admissible vectors
| Autor: | Alberti, Giovanni S., De Mari, Filippo, De Vito, Ernesto, Mantovani, Lucia |
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| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | Monatsh. Math., 173(3):261-307, 2014 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00605-013-0542-x |
| Popis: | In part I we introduced the class ${\mathcal E}_2$ 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 Calder\'on equation. They include products of 1D-wavelets, directional wavelets, shearlets, and many new examples. Comment: 37 pages, 3 figures |
| Databáze: | arXiv |
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