Abstract shearlet transform
Approximately ten years ago the generalization of wavelets to shearlets started its development. This paper extends shearlets (introduced in 2005 to find efficient extensions for the classical wavelet transform, see among others \textit{G. Kutyniok} and \textit{D. Labate} [``Construction of regular and irregular shearlet frames'', J. Wavelet Theory Appl. 1, No. 1, 1--12 (2007)] from Euclidean spaces to locally compact groups. The layout of the paper is as follows: \S1. { Introduction} \quad Gives an overview of the developments. \S2. { Preliminaries and notations} \quad Introducing the semidirect product \(G=H\times_{\tau}K\) of locally compact groups (\(h\mapsto \tau_h\) being a homeomorphism of \(H\) into the group \(\Aut(K)\) of automorphisms of \(K\); \((h,k)\mapsto \tau_h(k)\) from \(H\times K\) into \(K\) assumed continuous) and the left Haar measure on \(G\). \S3. { Main results} \quad Here, three locally compact groups play a role and the results are given in Theorems 3.4, 3.5 and 3.9. \S4. { Examples} \quad In this section, six different examples are given. \hskip0.6cm { References} \quad Contains 20 items (18 of which date from years after 2004).
scientific article; zbMATH DE number 6538896