caa a22 4500 463246896 CHVBK 20180405153328.0 cr unu---uuuuu 170326e20070801xx s 000 0 eng 10.1007/s00041-006-6901-4 doi (NATIONALLICENCE)springer-10.1007/s00041-006-6901-4 Frames and Coorbit Theory on Homogeneous Spaces with a Special Guidance on the Sphere [Elektronische Daten] [Stephan Dahlke, Gabriele Steidl, Gerd Teschke] The topic of this article is a generalization of the theory of coorbit spaces and related frame constructions to Banach spaces of functions or distributions over domains and manifolds. As a special case one obtains modulation spaces and Gabor frames on spheres. Group theoretical considerations allow first to introduce generalized wavelet transforms. These are then used to define coorbit spaces on homogeneous spaces, which consist of functions having their generalized wavelet transform in some weighted Lp space. We also describe natural ways of discretizing those wavelet transforms, or equivalently to obtain atomic decompositions and Banach frames for the corresponding coorbit spaces. Based on these facts we treat aspects of nonlinear approximation and show how the new theory can be applied to the Gabor transform on spheres. For the S1 we exhibit concrete examples of admissible Gabor atoms which are very closely related to uncertainty minimizing states. Birkhauser Boston, 2007 Dahlke Stephan Universität Marburg, Fachbereich Mathematik und Informatik, Hans-Meerwein-Str., Lahnberge, 35032 Marburg, Germany aut Steidl Gabriele Universität Mannheim, Fakultät für Mathematik, und Informatik, A5, 68131 Mannheim, Germany aut Teschke Gerd Zuse-Institute-Berlin (ZIB), Takustr. 7, 14195 Berlin, Germany aut Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/4(2007-08-01), 387-403 1069-5869 13:4<387 2007 13 41 https://doi.org/10.1007/s00041-006-6901-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00041-006-6901-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dahlke Stephan Universität Marburg, Fachbereich Mathematik und Informatik, Hans-Meerwein-Str., Lahnberge, 35032 Marburg, Germany aut NATIONALLICENCE 700 1- Steidl Gabriele Universität Mannheim, Fakultät für Mathematik, und Informatik, A5, 68131 Mannheim, Germany aut NATIONALLICENCE 700 1- Teschke Gerd Zuse-Institute-Berlin (ZIB), Takustr. 7, 14195 Berlin, Germany aut NATIONALLICENCE 773 0- Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/4(2007-08-01), 387-403 1069-5869 13:4<387 2007 13 41 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer