Shearlet coorbit spaces and associated Banach frames

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Shearlet Coorbit Spaces: Compactly Supported Analyzing Shearlets, Traces and Embeddings (2011, background): “The following result from [6] shows that the unitary representation π defined in (1) is a squareintegrable representation of S.”
Full length article: Compactly supported shearlets are optimally sparse (2011, unknown): “[3] S.”
Fast Finite Shearlet Transform: a tutorial (2012, background): “Moreover, similarly as wavelets are related to Besov spaces via atomic decompositions, shearlets correspond to certain function spaces, the so-called shearlet coorbit spaces [5].”
Generalized coorbit space theory and inhomogeneous function spaces of Besov-Lizorkin-Triebel type (2010, methodology): “, the recent shearlet spaces [13] as well as modulation spaces.”
Coorbit spaces and wavelet coefficient decay over general dilation groups (2012, methodology): “Many results in this paper have shearlet counterparts in the literature (e.g. in [7,8]) that typically are similar in spirit but do not exactly match in terms of the required assumptions.”