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On dual shearlet frames. (English) Zbl 1412.42080

Summary: In This paper, we give a necessary condition for function in \(L^2\) with its dual to generate a dual shearlet tight frame with respect to admissibility.

MSC:

42C15 General harmonic expansions, frames
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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References:

[1] C. K. Chui, X. Shi, On a LittlewoodPaley identity and characterization of wavelets, Math. Anal. Appl. 177 (1993) 608-626. · Zbl 0782.42025
[2] I. Daubechies, B. Han, Pairs of dual wavelet frames from any two renable functions, Constr. Appr.,to appear. · Zbl 1055.42025
[3] B. Han, On dual wavelet tight frames, Appl. Comput. Harmon. Anal. 4 (1997) 380-413. · Zbl 0880.42017
[4] G. Kutyniok, D. Labate, Shearlets: Multiscale Analysis for Multivariate Data, Birkhauser, Basel, 2012. · Zbl 1237.42001
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