Continuous wavelet transforms with Abelian dilation groups

DOI10.1063/1.532480zbMath0929.42028OpenAlexW2171092394MaRDI QIDQ4701631

Hartmut Führ

Publication date: 21 November 1999

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.532480

zbMATH Keywords

semidirect productcontinuous wavelet transformsAbelian matrix groupsgroups of commutative associative algebras

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Coherent states (81R30) Other representations of locally compact groups (22D12)

Related Items (14)

CONTINUOUS ACTION OF LIE GROUPS ON ℝⁿ AND FRAMES ⋮ Classifying decomposition and wavelet coorbit spaces using coarse geometry ⋮ Simplified vanishing moment criteria for wavelets over general dilation groups, with applications to abelian and shearlet dilation groups ⋮ Embeddings of shearlet coorbit spaces into Sobolev spaces ⋮ Coorbit spaces and wavelet coefficient decay over general dilation groups ⋮ A classification of continuous wavelet transforms in dimension three ⋮ Recent Progress in Shearlet Theory: Systematic Construction of Shearlet Dilation Groups, Characterization of Wavefront Sets, and New Embeddings ⋮ Sampling in reproducing kernel Banach spaces on Lie groups ⋮ Cone-Adapted Shearlets and Radon Transforms ⋮ Coorbit spaces associated to integrably admissible dilation groups ⋮ Unitarization and Inversion Formulae for the Radon Transform Between Dual Pairs ⋮ The Radon transform intertwines wavelets and shearlets ⋮ Characterizing abelian admissible groups ⋮ Unitarization of the Horocyclic Radon Transform on Symmetric Spaces

Cites Work

• Two-dimensional directional wavelets and the scale-angle representation
• Elementary structure of real algebraic varieties
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• On the regular representation of a nonunimodular locally compact group
• A wavelet transform for the Poincaré group
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• Coherent states for n-dimensional Euclidean groups E(n) and their application
• Wavelets associated with representations of the affine Weyl–Heisenberg group
• COHERENT STATES AND THEIR GENERALIZATIONS: A MATHEMATICAL OVERVIEW
• Wavelet frames and admissibility in higher dimensions
• Continuous Representation Theory Using the Affine Group

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