【摘 要】
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One of the main challenges of frame and wavelet theory is to construct and analyzesuitable frames which provide sparse representations for natural classes o
【机 构】
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UniversityofDelaware,USA
【出 处】
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算子代数和调和分析2017年研讨会 (Workshop on Operator Algebras and Harmoni
论文部分内容阅读
One of the main challenges of frame and wavelet theory is to construct and analyzesuitable frames which provide sparse representations for natural classes of square-integrable functions on the Euclidean space Rd.A frame for L2(Rd) is a sequence {ej}j∈J in L2(Rd)together with constants 0< A≤B<∞ such that A‖f‖22≤Σj∈J〈f,ej〉≤B‖f‖22;for all f∈L2(Rd).The construction of frames in higher dimensions turns out to be a difficulttask.In this talk we present an explicit frame construction based on earlier work of Bernier andTaylor in 1996,where a general framework for the construction of higher dimensional continuouswavelet transforms was outlined.We then use the geometric features of the ambient spaceto produce frames with small frame bound gap.This talk is based on joint work with KrisHollingsworth,and Nathaniel Kim,Aizhan Syzdykova,and Keith F.Taylor.
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