Publications de l'Institut Mathematique 2023 Volume 113, Issue 127, Pages: 121-129
https://doi.org/10.2298/PIM2327121A
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Characterization of tight wavelet frames with composite dilations in L2(Rn)
Ahmad Owais (Department of Mathematics, National Institute of Technology, Srinagar, Jammu and Kashmir, India), siawoahmad@gmail.com
Tight wavelet frames are different from the orthonormal wavelets because of
redundancy. By sacrificing orthonormality and allowing redundancy, the tight
wavelet frames become much easier to construct than the orthonormal
wavelets. Guo, Labate, Lim, Weiss, and Wilson [Electron. Res. Announc. Am.
Math. Soc. 10 (2004), 78-87] introduced the theory of wavelets with
composite dilations in order to provide a framework for the construction of
waveforms defined not only at various scales and locations but also at
various orientations. In this paper, we provide the characterization of
composite wavelet system to be tight frame for L2(Rn).
Keywords: wavelet frame, composite dilation, Fourier transform
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