Examples of Coorbit Spaces for Dual Pairs
نویسنده
چکیده
In this paper we summarize and give examples of a generalization of the coorbit space theory initiated in the 1980’s by H.G. Feichtinger and K.H. Gröchenig. Coorbit theory has been a powerful tool in characterizing Banach spaces of distributions with the use of integrable representations of locally compact groups. Examples are a wavelet characterization of the Besov spaces and a characterization of some Bergman spaces by the discrete series representation of SL2(R). We present examples of Banach spaces which could not be covered by the previous theory, and we also provide atomic decompositions for an example related to a non-integrable representation.
منابع مشابه
Coorbit Spaces for Dual Pairs
In this paper we present an abstract framework for construction of Banach spaces of distributions from group representations. This generalizes the theory of coorbit spaces initiated by H.G. Feichtinger and K. Gröchenig in the 1980’s. Spaces that can be described by this new technique include the whole Banach-scale of Bergman spaces on the unit disc. For these Bergman spaces we show that atomic ...
متن کاملGeneralized coorbit space theory and inhomogeneous function spaces of Besov-Lizorkin-Triebel type
Coorbit space theory is an abstract approach to function spaces and their atomic decompositions. The original theory developed by Feichtinger and Gröchenig in the late 1980ies heavily uses integrable representations of locally compact groups. Their theory covers, in particular, homogeneous Besov-Lizorkin-Triebel spaces, modulation spaces, Bergman spaces and the recent shearlet spaces. However, ...
متن کاملG-continuous Frames and Coorbit Spaces
A generalized continuous frame is a family of operators on a Hilbert space H which allows reproductions of arbitrary elements of H by continuous superpositions. Generalized continuous frames are natural generalization of continuous and discrete frames in Hilbert spaces which include many recent generalization of frames. In this article,we associate to a generalized continuous frame suitable Ban...
متن کاملBanach frames in coorbit spaces consisting of elements which are invariant under symmetry groups
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-Gröchenig the...
متن کاملFrames and Coorbit Theory on Homogeneous Spaces with a Special Guidance on the Sphere
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 ...
متن کامل