AB-wavelet frames in L2(Rn)
Keyword(s):
In order to provide a unified treatment for the continuum and digital realm of multivariate data, Guo, Labate, Weiss and Wilson [Electron. Res. Announc. Amer. Math. Soc. 10 (2004), 78-87] introduced the notion of AB-wavelets in the context of multiscale analysis. We continue and extend their work by studying the frame properties of AB-wavelet systems {DADBTk??(k ? Zn; 1 <? ? <? L)}in L2(Rn). More precisely, we establish four theorems giving su_cient conditions under which the AB-wavelet system constitutes a frame for L2(Rn). The proposed conditions are stated in terms of the Fourier transforms of the generating functions.
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2014 ◽
Vol 57
(2)
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pp. 254-263
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2006 ◽
Vol 58
(6)
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pp. 1121-1143
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2015 ◽
Vol 27
(04)
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pp. 1550007
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2008 ◽
Vol 06
(02)
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pp. 183-208
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1989 ◽
Vol 8
(4)
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pp. 229-236
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2014 ◽
Vol 1079-1080
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pp. 878-881
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