Equivalence of the metaplectic representation with sums of wavelet representations for a class of subgroups of the symplectic group

DOI10.1007/s00041-012-9244-3zbMath1309.22006OpenAlexW2008797285MaRDI QIDQ485121

Eckart Schulz, Kampanat Namngam

Publication date: 9 January 2015

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00041-012-9244-3

zbMATH Keywords

symplectic groupwavelet transformmetaplectic representationaffine representationadmissible vectors

Mathematics Subject Classification ID

Unitary representations of locally compact groups (22D10) General harmonic expansions, frames (42C15)

Related Items (3)

Reproducing subgroups of \(\mathrm{Sp}(2,\mathbb R)\). II: Admissible vectors ⋮ Extensions of the Heisenberg group by one‐parameter groups of dilations which are subgroups of the affine and the symplectic groups ⋮ Two-dimensional Shannon type expansions via one-dimensional affine and wavelet lattice actions

Cites Work

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• Foundations of time-frequency analysis
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• Admissible vectors for mock metaplectic representations
• Analytic features of reproducing groups for the metaplectic representation
• Generalized Calderón conditions and regular orbit spaces
• Dimensional upper bounds for admissible subgroups for the metaplectic representation
• Harmonic Analysis in Phase Space. (AM-122)
• Wavelets from Square-Integrable Representations
• Wavelet frames and admissibility in higher dimensions
• CONTINUOUS ACTION OF LIE GROUPS ON ℝⁿ AND FRAMES

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