期刊
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
卷 13, 期 4, 页码 387-404出版社
BIRKHAUSER BOSTON INC
DOI: 10.1007/s00041-006-6901-4
关键词
square integrable group representations; time-frequency analysis; atomic decompositions; (Banach) frames; homogeneous spaces; weighted coorbit spaces.
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 L-p 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 S-1 we exhibit concrete examples of admissible Gabor atoms which art very closely related to uncertainty minimizing states.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据