Dimensional upper bounds for admissible subgroups for the metaplectic representation

DOI10.1002/mana.200710062zbMath1198.22002OpenAlexW2159454297MaRDI QIDQ3585613

Anita Tabacco, Elena Cordero, Krzysztof Nowak, Filippo de Mari

Publication date: 20 August 2010

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.200710062

zbMATH Keywords

waveletsJacobi groupmetaplectic representationWigner distributionreproducing formula

Mathematics Subject Classification ID

Unitary representations of locally compact groups (22D10) Other transforms and operators of Fourier type (43A32)

Related Items (14)

Different faces of the shearlet group ⋮ On Some Characterization of Generalized Representation Wave-Packet Frames Based on Some Dilation Group ⋮ The Use of Representations in Applied Harmonic Analysis ⋮ Continuous and discrete frames generated by the evolution flow of the Schrödinger equation ⋮ Geometric classification of semidirect products in the maximal parabolic subgroup of Sp(2, ℝ) ⋮ Square-integrability of multivariate metaplectic wave-packet representations ⋮ Cone-Adapted Shearlets and Radon Transforms ⋮ Equivalence of the metaplectic representation with sums of wavelet representations for a class of subgroups of the symplectic group ⋮ Anisotropic shearlet transforms for L² ⋮ Extensions of the Heisenberg group by one‐parameter groups of dilations which are subgroups of the affine and the symplectic groups ⋮ Strichartz estimates for the metaplectic representation ⋮ Discrete frames for \(L^2(\mathbb{R}^{n^2})\) arising from tiling systems on \(\mathrm{GL}_n(\mathbb{R})\) ⋮ Two-dimensional Shannon type expansions via one-dimensional affine and wavelet lattice actions ⋮ Weak-Type Estimates for the Metaplectic Representation Restricted to the Shearing and Dilation Subgroup of $$SL(2,\mathbb {R})$$

Cites Work

• A characterization of the higher dimensional groups associated with continuous wavelets.
• Coherent states, wavelets and their generalizations
• Analytic features of reproducing groups for the metaplectic representation
• Analysis of the affine transformations of the time-frequency plane
• Wavelets from Square-Integrable Representations

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