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Banach frames in coorbit spaces consisting of elements which are invariant under symmetry groups

机译:Coorbit空间中的Banach框架由对称组下不变的元素组成

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This paper is concerned with the construction of atomic decompositions and Banach frames for subspaces of certain Banach spaces consisting of elements which are invariant under some symmetry group. These Banach spaces—called coorbit spaces—are related to an integrable group representation. The construction is established via a generalization of the well-established Feichtinger-Groechenig theory. Examples include radial wavelet-like atomic decompositions and frames for radial Besov-Triebel-Lizorkin spaces, as well as radial Gabor frames and atomic decompositions for radial modulation spaces.
机译:本文关注的是某些Banach空间的子空间的原子分解和Banach框架的构造,该子空间由在某些对称组下不变的元素组成。这些Banach空间(称为Coorbit空间)与可积组表示有关。通过公认的费希丁格-格罗申尼格理论的概括来确定构造。示例包括用于径向Besov-Triebel-Lizorkin空间的径向小波状原子分解和框架,以及用于径向调制空间的径向Gabor框架和原子分解。

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