Shearlet Coorbit Spaces: Compactly Supported Analyzing Shearlets, Traces and Embeddings
نویسندگان
چکیده
منابع مشابه
Shearlet Coorbit Spaces: Compactly Supported Analyzing Shearlets, Traces and Embeddings
We show that compactly supported functions with sufficient smoothness and enough vanishing moments can serve as analyzing vectors for shearlet coorbit spaces. We use this approach to prove embedding theorems for subspaces of shearlet coorbit spaces resembling shearlets on the cone into Besov spaces. Furthermore, we show embedding relations of traces of these subspaces with respect to the real a...
متن کاملShearlet Coorbit Spaces: Traces and Embeddings in Higher Dimensions – Extended Version
This papers examines structural properties of the recently developed shearlet coorbit spaces in higher dimensions. We prove embedding theorems for subspaces of shearlet coorbit spaces resembling shearlets on the cone in three dimensions into Besov spaces. The results are based on general atomic decompositions of Besov spaces. Furthermore, we establish trace results for these subspaces with resp...
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Shearlet theory has become a central tool in analyzing and representing 2D data with anisotropic features. Shearlet systems are systems of functions generated by one single generator with parabolic scaling, shearing, and translation operators applied to it, in much the same way wavelet systems are dyadic scalings and translations of a single function, but including a precise control of directio...
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In this paper, we study the relationships of the newly developed continuous shearlet transform with the coorbit space theory. It turns out that all the conditions that are needed to apply the coorbit space theory can indeed be satisfied for the shearlet group. Consequently, we establish new families of smoothness spaces, the shearlet coorbit spaces. Moreover, our approach yields Banach frames f...
متن کاملMultivariate Shearlet Transform, Shearlet Coorbit Spaces and their Structural Properties
This chapter is devoted to the generalization of the continuous shearlet transform to higher dimensions as well as to the construction of associated smoothness spaces and to the analysis of their structural properties, respectively. To construct canonical scales of smoothness spaces , so-called shearlet coorbit spaces , and associated atomic decompositions and Banach frames we prove that the ge...
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ژورنال
عنوان ژورنال: Journal of Fourier Analysis and Applications
سال: 2011
ISSN: 1069-5869,1531-5851
DOI: 10.1007/s00041-011-9181-6