Equivalence of the metaplectic representation with sums of wavelet representations for a class of subgroups of the symplectic group
type: Item
instance of: scholarly article
title: Equivalence of the metaplectic representation with sums of wavelet representations for a class of subgroups of the symplectic group
zbMATH Open document ID: 1309.22006
author: Kampanat Namngam
author: Eckart Schulz
published in: The Journal of Fourier Analysis and Applications
publication date: 2015-01-09T00:00:00Z
review text: 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.
reviewed by: Franz Luef
Mathematics Subject Classification ID: 22D10
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 6384904
zbMATH Keywords: metaplectic representation
zbMATH Keywords: admissible vectors
zbMATH Keywords: wavelet transform
zbMATH Keywords: symplectic group
zbMATH Keywords: affine representation
MaRDI profile type: Publication
full work available at URL: s00041-012-9244-3
OpenAlex ID: W2008797285
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DOI: 10.1007/S00041-012-9244-3
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description: scientific article; zbMATH DE number 6384904