Reproducing subgroups of \(\mathrm{Sp}(2,\mathbb R)\). II: Admissible vectors

DOI10.1007/s00605-013-0542-xzbMath1305.42034arXiv1212.2743OpenAlexW1531158252MaRDI QIDQ2447915

Ernesto De Vito, Giovanni S. Alberti, Lucia Mantovani, Filippo de Mari

Publication date: 29 April 2014

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.2743

zbMATH Keywords

waveletsmetaplectic representationreproducing formulaadmissible vectors

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) (43A65) General properties and structure of real Lie groups (22E15) Other transforms and operators of Fourier type (43A32) Analysis on other specific Lie groups (43A80)

Related Items (9)

The Use of Representations in Applied Harmonic Analysis ⋮ A classification of continuous wavelet transforms in dimension three ⋮ 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) ⋮ Recent Progress in Shearlet Theory: Systematic Construction of Shearlet Dilation Groups, Characterization of Wavefront Sets, and New Embeddings ⋮ Square-integrability of multivariate metaplectic wave-packet representations ⋮ Coorbit spaces with voice in a Fréchet space ⋮ Two-dimensional Shannon type expansions via one-dimensional affine and wavelet lattice actions ⋮ Unitarization and Inversion Formulae for the Radon Transform Between Dual Pairs

Cites Work

• Equivalence of the metaplectic representation with sums of wavelet representations for a class of subgroups of the symplectic group
• Reproducing subgroups of \(Sp(2,\mathbb{R})\). I: Algebraic classification
• Admissible vectors for mock metaplectic representations
• Transformation groups and \(C^ *\)-algebras
• Analysis of the affine transformations of the time-frequency plane
• Isotropic Shearlet Analogs forL²(ℝ^k) and Localization Operators
• Harmonic Analysis in Phase Space. (AM-122)
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