Characterization of Tight Wavelet Frames With Composite Dilations in $L^2(\mathbb R^n)$

Owais Ahmad

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. extbf{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 $L^2(\mathbb R^n)$