We introduce the notion of admissible subgroup H of G = Hd Sp(d, R) relative to the (extended) metaplectic representation μe via the Wigner distribution. Under mild additional assumptions, it is shown to be equivalent to the fact that the identity f = H ⟨f, μe(h)φ⟩μe(h)φ dh holds (weakly) for all f ∈ L2(Rd). We use this equivalence to exhibit classes of admissible subgroups of Sp(2, R). We also establish some connections with wavelet theory, i.e., with curvelet and contourlet frames.
Analytic features of reproducing groups for the metaplectic representation
DE MARI CASARETO DAL VERME, F.;
2006-01-01
Abstract
We introduce the notion of admissible subgroup H of G = Hd Sp(d, R) relative to the (extended) metaplectic representation μe via the Wigner distribution. Under mild additional assumptions, it is shown to be equivalent to the fact that the identity f = H ⟨f, μe(h)φ⟩μe(h)φ dh holds (weakly) for all f ∈ L2(Rd). We use this equivalence to exhibit classes of admissible subgroups of Sp(2, R). We also establish some connections with wavelet theory, i.e., with curvelet and contourlet frames.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.