We introduce the notion of admissible subgroup H of G = H^d \rtimes Sp(d,R) relative to the (extended) metaplectic representation μ_e via the Wigner distribution. Under mild additional assumptions, it is shown to be equivalent to the fact that the identity f= \int_H \la f,μ_e(h) φ \ra μ_e(h) φ dh holds (weakly) for all f ∈ L^2(R^d ). 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 / E., Cordero; F., DE MARI; K., Nowak; Tabacco, Anita Maria. - In: JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS. - ISSN 1069-5869. - 12:(2006), pp. 157-180.

Analytic features of reproducing groups for the metaplectic representation

TABACCO, Anita Maria
2006

Abstract

We introduce the notion of admissible subgroup H of G = H^d \rtimes Sp(d,R) relative to the (extended) metaplectic representation μ_e via the Wigner distribution. Under mild additional assumptions, it is shown to be equivalent to the fact that the identity f= \int_H \la f,μ_e(h) φ \ra μ_e(h) φ dh holds (weakly) for all f ∈ L^2(R^d ). 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/1406327
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