Equivalence of the metaplectic representation with sums of wavelet representations for a class of subgroups of the symplectic group
In a series of papers Cordero, De Mari, Nowak and Tabacco have characterized the admissibility of vectors for the extended metaplectic representation of closed subgroups of \(\mathbb{R}^n\rtimes\mathrm{Sp}(n,\mathbb{R})\) in terms of the Wigner transform. The paper under review extends their results and allows a larger family of admissible vectors and more general subgroups as the aforementioned results. For a class of subgroups of \(\mathrm{Sp}(n,\mathbb{R})\) the equivalence of the metaplectic representation with a sum of wavelet representations is demonstrated and also used in the demonstrations of the main results of this interesting and well-written paper.
scientific article; zbMATH DE number 6384904
scientific article