COORBIT SPACE THEORY FOR THE TOEPLITZ SHEARLET TRANSFORM

DOI10.1142/S0219691312500373zbMath1252.42031OpenAlexW2083547436MaRDI QIDQ3164783

Sören Häuser, Gerd Teschke, Stephan Dahlke

Publication date: 16 October 2012

Published in: International Journal of Wavelets, Multiresolution and Information Processing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219691312500373

zbMATH Keywords

Lie groupsatomic decompositionsBanach framescoorbit spacescoorbit space theorysquare-integrable group representationsshearlet transformshear matrixToeplitz shearlet transform

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Linear symmetric and selfadjoint operators (unbounded) (47B25) Unitary representations of locally compact groups (22D10) General harmonic expansions, frames (42C15)

Related Items (16)

Translation and modulation invariant Banach spaces of tempered distributions satisfy the metric approximation property ⋮ Different faces of the shearlet group ⋮ Shearlet Coorbit Theory ⋮ Structured, compactly supported Banach frame decompositions of decomposition spaces ⋮ 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 ⋮ A classification of continuous wavelet transforms in dimension three ⋮ Embeddings of Decomposition Spaces ⋮ Dilational symmetries of decomposition and coorbit spaces ⋮ Recent Progress in Shearlet Theory: Systematic Construction of Shearlet Dilation Groups, Characterization of Wavefront Sets, and New Embeddings ⋮ From Frazier-Jawerth characterizations of Besov spaces to wavelets and decomposition spaces ⋮ Frames arising from irreducible solvable actions. I. ⋮ Smoothness of weak solutions under linear partial differential operators with constant coefficients via the convergence of then-dimensional continuous shearlet transform ⋮ Compactly supported bounded frames on Lie groups ⋮ Coorbit Theory and Bergman Spaces

Cites Work

• Banach spaces related to integrable group representations and their atomic decompositions. I
• Banach spaces related to integrable group representations and their atomic decompositions. II
• Shearlet coorbit spaces and associated Banach frames
• The continuous shearlet transform in arbitrary space dimensions
• Describing functions: Atomic decompositions versus frames
• SHEARLET TRANSFORMS AND DIRECTIONAL REGULARITIES
• THE UNCERTAINTY PRINCIPLE ASSOCIATED WITH THE CONTINUOUS SHEARLET TRANSFORM
• Ridgelets: a key to higher-dimensional intermittency?

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