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

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.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/645565
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 10
  • ???jsp.display-item.citation.isi??? 9
social impact